Exponents

Last Updated on February 14, 2024.

When numbers are expressed in the form a^b, then we call b the exponent. Exponents indicate the number of times bases are used as factors. Power and exponent mean the same things.

The expression a to the power m (or a^m) is defined to mean: a^m = a・ a ・a ・ a … (m times). Here, our number “a” is what we call the base of the exponential expression, while the number “m” is called the exponent.

1. Evaluate \(3^{5}\)

Use your calculator.

A.243

B.15

C.30

D.115

Question 1 of 2

2. Evaluate \(15^{3}\)

Use your calculator.

A.125

B.3,375

C.3,300

D.104

Question 2 of 2

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This lesson is provided by Onsego GED Prep.

Video Transcription

The exponent, our number “m” is telling us to repeat our base “a” as a factor “m” times.

So let’s get going with 10³.

Our base is 10 (ten), meaning that 10 (ten) is a factor and that it is going to be multiplied by 10 (itself) a number of times.

This number of times is indicated by our exponent (the number in superscript). Well, here, our exponent is three (3), meaning that our base of 10 (ten) is going to be used as a factor three (3) times.

So we have 10^3, which means: 10 • 10 • 10.

So now we’ve seen what 10³ stands for, or means, but how should we pronounce this?

We have lots of choices. The term could be pronounced as “ten (10) raised to the 3rd power,” or “ten (10) to the 3rd,” or also “ten (10) cubed.”

The phrase “raised to a power” is inserted between our base and our exponent to mark exponential notation.

Let’s look at another example:

Evaluate this expression: 2³・ 3² ・ 5²

First, we need to raise each of the factors to the given exponent. Then, we can perform multiplication in order from left to right.

2³ ・ 3² ・ 5² = 8・ 9 ・ 25 which equals: 72・ 25 = 1800

The GED Math subtest is always including questions with exponents. Make sure that you’ll be familiar with lessons related to exponents and the rules of exponents.

So when numbers are expressed like “a^b”, we call b the exponent. Exponents are indicating the number of times the bases are used as factors. Exponent and Power mean the same things.