Exponents: What are they and how do we use them?

What is an Exponent?

An exponent is simply the amount of times a number is multiplied by itself.

What you will notice is that when a number is multiplied by itself, it can grow—”exponentially.” Exponential growth is faster than linear growth (things that grow in a straight line) and it is often used in scientific explanations of how things work in nature. So, keep abreast of exponents and what they are used for because you will see them again in various math classes, in science classes and in other disciplines like finance.

There are a few rules to get use to when working with exponents—exponents can also be referred to as powers.

Multiplication Rules

When you’re multiplying powers with the same base, just add the exponents:

When finding the power of a power, multiply the exponents:

When finding the power of a product, just figure the power of each term and multiply them:

Negative Exponents and 0

Any number (other than zero), raised to the zero power is 1:

A number raised to a negative power should be solved using its reciprocal:

Division Rules

When dividing powers with the same base, subtract the exponents:

When finding the power of a quotient, figure out the power of the numerator, then the denominator and finally divide:

Summary

Keep in mind that these rules apply to variables—even when you are working with expressions that have many different factors, these rules apply.