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# Difference Between Exponent and Power

July 11, 2022

This post is also available in: हिन्दी (Hindi)

As a student you’ve been using exponents and powers to represent very big or very small numbers or to solve multiplication problems in mathematics.

Did you know what exactly is the difference between exponent and power?

These types of operations involve two numbers that can be written as $x^{a}$, where $x$ is the base number, and $a$ is the exponent. The whole expression is known as “power” and written as “$x$ to the power of $a$” where $a$ is any positive integer.

## What is Power?

Let’s first see what power means. Power is a mathematical expression that can be used to represent exactly how many times a number should be used in a multiplication process. In simple words, it is an expression that describes repeated multiplication of the same given number. Power in mathematics is written as “raising a number to any other number”.

So, power is used to represent the whole expression. For example, $4 \times 4 \times 4$ which is equal to $64$ and is written as $4^{3}$. Here the whole expression $4^{3}$ is called power.

## What is an Exponent?

Now moving on to exponent. Although It is generally used interchangeably with power, it is used in a different context. But the exponent is the superscript placed above to the right of the base of any number. Exponent is defined as a positive or negative number which represents the power to which the base number is raised meaning it states the number of times a number needs to be used in a multiplication process.

Again in the example above, $4^{3} = 4 \times 4 \times 4$, the $4$ is the base and $3$ is the power.

## Conclusion

Exponent and power are terms used when a number is multiplied by itself a specific number of times. The difference between exponents and power is an extremely minor observation that most of the time is neglected. There is a very thin line of difference between exponent and power.

## Practice Problems

1. Indicate the base and exponent. What is the power of the expression?
1. $11 \times 11 \times 11$
2. $-5 \times \left(-5 \right) \times \left(-5\right) \times \left(-5\right) \times \left(-5\right)$
3. $\left(\frac{2}{3} \right) × \left(\frac{2}{3} \right) × \left(\frac{2}{3} \right) × \left(\frac{2}{3} \right)$
2. Find the value of
1. $5^{3}$
2. $\left( \frac{3}{2} \right)^{3}$
3. $-2^{4}$
4. $\left( -3 \right)^{5}$
5. $\left( -4 \right)^{4}$
6. $\left(0.2 \right)^{3}$
7. $3^{-2}$