# Exponent vs. Power: Know the Difference

By Shumaila Saeed || Published on January 31, 2024

**An exponent refers to the number that indicates how many times a base is multiplied by itself, while power is the result of this multiplication.**

## Key Differences

An exponent is a mathematical notation indicating the number of times a number (the base) is multiplied by itself. Power, in contrast, refers to the actual product of this multiplication.

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Jan 31, 2024

Exponents are often represented as a small number written slightly above and to the right of the base number. They are key in expressing large numbers compactly. Power, however, represents the value obtained from the exponentiation process and can vary greatly depending on the base and exponent values.

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Jan 31, 2024

The concept of an exponent is foundational in mathematics, especially in algebra, where it simplifies the representation of repeated multiplication. Power, on the other hand, plays a crucial role in various mathematical calculations, such as in exponential growth and decay problems.

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Jan 31, 2024

Exponents can be integers, fractions, or even negative numbers, each changing how multiplication is carried out. For instance, a negative exponent implies division. Power, as a result of these varied exponent types, can take different forms like whole numbers, fractions, or decimals.

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Jan 31, 2024

In summary, an exponent is a way to express how many times a base is used in multiplication, while power is the actual numerical value resulting from this operation.

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Jan 31, 2024

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## Comparison Chart

### Definition

Number indicating how many times the base is multiplied by itself

The result of raising a base to an exponent

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### Notation

Written as a small number above and to the right of the base

Expressed as the whole expression,

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### Role in Mathematics

Indicates repetition in multiplication

Represents the value obtained from exponentiation

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### Variability

Can be an integer, fraction, or negative number

Value changes based on the base and exponent

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## Exponent and Power Definitions

#### Exponent

An exponent is an index that shows the degree of a mathematical operation.

The exponent in x^2 denotes that x is raised to the power of 2, or squared.

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#### Power

Power refers to a mathematical expression involving a base raised to an exponent.

In the equation 2^5 = 32, the power consists of the base 2 and the exponent 5.

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#### Exponent

An exponent is a superscript number indicating the scale of measurement in scientific notation.

In 3.0 x 10^8 meters, the exponent 8 represents the order of magnitude in meters.

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#### Power

In physics, power signifies the rate at which energy is transferred or work is done.

The electric motor's power output is 500 watts, allowing it to perform tasks efficiently.

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#### Exponent

An exponent is a small number or symbol indicating repeated multiplication.

In 2^4, the exponent 4 represents four repeated multiplications of 2.

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#### Power

Power can represent the influence or impact of an individual or entity in a particular domain.

His knowledge and expertise in the field have given him significant power within the scientific community.

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#### Exponent

An exponent represents the number of times a base is raised to a certain power.

10^3 equals 1,000, as the exponent 3 indicates three times the multiplication of 10.

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#### Power

The ability or capacity to act or do something effectively

Is it in your power to undo this injustice?.

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#### Power

Often powers A specific capacity, faculty, or aptitude

Her powers of concentration.

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#### Exponent

One that speaks for, represents, or advocates

Our senator is an exponent of free trade.

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#### Power

Physical strength or force exerted or capable of being exerted

The power of the waves.

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#### Exponent

Abbr. exp(Mathematics) A number or symbol, as 3 in (x + y)3, placed to the right of and above another number, symbol, or expression, denoting the power to which that number, symbol, or expression is to be raised. Also called power.

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#### Power

Effectiveness at moving one's emotions or changing how one thinks

A novel of great power.

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#### Power

The ability or official capacity to exercise control; authority

How long has that party been in power?.

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#### Power

The military strength or economic or political influence of a nation or other group

That country projects its power throughout the region.

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#### Exponent

(mathematics) The number by which a value (called the base) is said to be raised to a power in exponentiation: for example, the $3$ in $2^3=8$.

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#### Power

A country, nation, or other political unit having great influence or control over others

The western powers.

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#### Exponent

The degree to which the root of a radicand is found, for example, the $2$ in $\backslash sqrt[2]r=b$.

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#### Power

Powers(Christianity) The sixth of the nine orders of angels in medieval angelology.

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#### Exponent

(computing) The part of a floating-point number that represents its exponent value.

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#### Power

The energy or motive force by which a physical system or machine is operated

Turbines turned by steam power.

A sailing ship driven by wind power.

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#### Exponent

A number, letter, or any quantity written on the right hand of and above another quantity, and denoting how many times the latter is repeated as a factor to produce the power indicated

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#### Power

The capacity of a system or machine to operate

A vehicle that runs under its own power.

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#### Exponent

One who, or that which, stands as an index or representative; as, the leader of a party is the exponent of its principles.

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#### Power

Electrical or mechanical energy, especially as used to assist or replace human energy.

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#### Power

Electricity supplied to a home, building, or community

A storm that cut off power to the whole region.

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#### Power

(Physics) The rate at which work is done, expressed as the amount of work per unit time and commonly measured in units such as the watt and horsepower.

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#### Power

The product of applied potential difference and current in a direct-current circuit.

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#### Exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself

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#### Power

The product of the effective values of the voltage and current with the cosine of the phase angle between current and voltage in an alternating-current circuit.

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#### Exponent

An exponent is a mathematical notation used for compactly expressing repeated operations.

The exponent in 5^0 simplifies to 1, indicating no multiplication.

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#### Power

(Statistics) In a statistical test, the probability of correctly rejecting the null hypothesis when it is false.

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#### Power

A measure of the magnification of an optical instrument, such as a microscope or telescope.

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#### Power

Chiefly Upper Southern US A large number or amount. See Note at powerful.

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#### Power

Of or relating to political, social, or economic control

A power struggle.

A power base.

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#### Power

Operated with mechanical or electrical energy in place of bodily exertion

A power tool.

Power car windows.

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#### Power

Of or relating to the generation or transmission of electricity

Power companies.

Power lines.

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#### Power

(Informal) Of or relating to influential business or professional practices

A pinstriped suit with a power tie.

Met with high-level executives at a power breakfast.

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#### Power

Physical force or strength.

He needed a lot of power to hit the ball out of the stadium.

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#### Power

Electricity or a supply of electricity.

After the pylons collapsed, this town was without power for a few days.

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#### Power

The strength by which a lens or mirror magnifies an optical image.

We need a microscope with higher power.

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#### Power

Any of the elementary forms or parts of machines: three primary (the lever, inclined plane, and pulley) and three secondary (the wheel-and-axle, wedge, and screw).

The mechanical powers

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#### Power

A measure of the effectiveness that a force producing a physical effect has over time. If linear, the quotient of: (force multiplied by the displacement of or in an object) ÷ time. If rotational, the quotient of: (force multiplied by the angle of displacement) ÷ time.

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#### Power

A product of equal factors (and generalizations of this notion): $x^n$, read as "$x$ to the power of $n$" or the like, is called a power and denotes the product $x\; \backslash times\; x\; \backslash times\; \backslash cdots\; \backslash times\; x$, where $x$ appears $n$ times in the product; $x$ is called the base and $n$ the exponent.

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#### Power

(statistics) The probability that a statistical test will reject the null hypothesis when the alternative hypothesis is true.

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#### Power

In Christian angelology, an intermediate level of angels, ranked above archangels, but exact position varies by classification scheme.

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#### Power

(transitive) To provide power for (a mechanical or electronic device).

This CD player is powered by batteries.

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#### Power

Ability to act, regarded as latent or inherent; the faculty of doing or performing something; capacity for action or performance; capability of producing an effect, whether physical or moral: potency; might; as, a man of great power; the power of capillary attraction; money gives power.

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#### Power

Ability, regarded as put forth or exerted; strength, force, or energy in action; as, the power of steam in moving an engine; the power of truth, or of argument, in producing conviction; the power of enthusiasm.

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#### Power

Capacity of undergoing or suffering; fitness to be acted upon; susceptibility; - called also passive power; as, great power of endurance.

Power, then, is active and passive; faculty is active power or capacity; capacity is passive power.

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#### Power

The exercise of a faculty; the employment of strength; the exercise of any kind of control; influence; dominion; sway; command; government.

Power is no blessing in itself but when it is employed to protect the innocent.

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#### Power

The agent exercising an ability to act; an individual invested with authority; an institution, or government, which exercises control; as, the great powers of Europe; hence, often, a superhuman agent; a spirit; a divinity.

And the powers of the heavens shall be shaken.

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#### Power

A military or naval force; an army or navy; a great host.

Never such a power . . . Was levied in the body of a land.

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#### Power

The rate at which mechanical energy is exerted or mechanical work performed, as by an engine or other machine, or an animal, working continuously; as, an engine of twenty horse power.

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#### Power

A mechanical agent; that from which useful mechanical energy is derived; as, water power; steam power; hand power, etc.

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#### Power

The product arising from the multiplication of a number into itself; as, a square is the second power, and a cube is third power, of a number.

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#### Power

A machine acted upon by an animal, and serving as a motor to drive other machinery; as, a dog power.

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#### Power

Mental or moral ability to act; one of the faculties which are possessed by the mind or soul; as, the power of thinking, reasoning, judging, willing, fearing, hoping, etc.

The guiltiness of my mind, the sudden surprise of my powers, drove the grossness . . . into a received belief.

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#### Power

The degree to which a lens, mirror, or any optical instrument, magnifies; in the telescope, and usually in the microscope, the number of times it multiplies, or augments, the apparent diameter of an object; sometimes, in microscopes, the number of times it multiplies the apparent surface.

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#### Power

An authority enabling a person to dispose of an interest vested either in himself or in another person; ownership by appointment.

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#### Power

Hence, vested authority to act in a given case; as, the business was referred to a committee with power.

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#### Power

Possession of controlling influence;

The deterrent power of nuclear weapons

The power of his love saved her

His powerfulness was concealed by a gentle facade

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#### Power

(physics) the rate of doing work; measured in watts (= joules/second)

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#### Power

Possession of the qualities (especially mental qualities) required to do something or get something done;

Danger heightened his powers of discrimination

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#### Power

(of a government or government official) holding an office means being in power;

Being in office already gives a candidate a great advantage

During his first year in office

During his first year in power

The power of the president

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#### Power

One possessing or exercising power or influence or authority;

The mysterious presence of an evil power

May the force be with you

The forces of evil

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#### Power

A mathematical notation indicating the number of times a quantity is multiplied by itself

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#### Power

Supply the force or power for the functioning of;

The gasoline powers the engines

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#### Power

Power represents the capacity to perform work or control circumstances.

The hydraulic system has the power to lift heavy objects effortlessly.

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#### Power

Power can denote political or authoritative control over a group or a situation.

The president holds the power to veto legislation passed by the congress.

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## Repeatedly Asked Queries

#### What does an exponent represent?

It represents the number of times a base is multiplied by itself.

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#### Is power always a larger number than the base?

Not necessarily, it depends on the base and exponent values.

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#### How do you calculate power?

By multiplying the base by itself as many times as indicated by the exponent.

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#### How is power different from an exponent?

Power is the result of the exponentiation process.

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#### What is the power of a number raised to zero?

It’s always 1, regardless of the base.

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#### Can power be a negative number?

Yes, if the base is negative and the exponent is an odd integer.

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#### Are exponents used in scientific notation?

Yes, to represent very large or small numbers compactly.

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#### Can exponents be used in geometry?

Yes, especially in formulas involving area and volume.

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#### What role do exponents play in algebra?

They simplify expressions involving repeated multiplication.

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#### How does an exponent affect a base of 1?

Any exponent of 1 results in 1 as the power.

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#### Is there a difference between even and odd exponents?

Yes, affecting the sign and behavior of the power.

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#### How does a negative base affect power?

The power alternates between positive and negative depending on the exponent.

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#### What is the significance of square and cube powers?

They represent a number multiplied by itself twice or thrice, respectively.

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#### Can exponents be irrational numbers?

Yes, though less common in basic mathematics.

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#### What happens when two powers with the same base are multiplied?

Their exponents are added.

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#### Is the concept of power used in finance?

Yes, especially in compound interest calculations.

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#### Are exponents relevant in exponential growth models?

Absolutely, they are fundamental in such models.

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About Author

Written by

Shumaila SaeedShumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.