Exponents

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.

This lesson is a part of Onsego GED Prep.

Video Transcription

An exponent tells us how many times the base is multiplied by itself. For example, in 2³, the number 2 is the base, and 3 is the exponent. That means:

2³ = 2 × 2 × 2 = 8

But don’t confuse this with regular multiplication. 2³ is not the same as 2 × 3, which would be 6. The exponent means repeated multiplication—not just multiplying two numbers.

Exponent Rules You Need to Know

The GED test often includes questions about exponents. Luckily, you only need a few simple rules to solve most of them.

Let’s review those now:

1. A number raised to the power of 1 stays the same.
   Example:
   6¹ = 6
2. Any number raised to the power of 0 is equal to 1.
   Example:
   6⁰ = 1
   145⁰ = 1
3. When multiplying numbers with the same base, keep the base and add the exponents.
   Example:
   6³ × 6⁴ = 6⁷ (because 3 + 4 = 7)
4. When dividing numbers with the same base, keep the base and subtract the exponents.
   Example:
   6⁹ ÷ 6³ = 6⁶ (because 9 − 3 = 6)
5. A negative exponent means the base moves to the denominator.
   Example:
   6⁻² = 1 / 6²

Let’s Try a GED-Style Problem

Simplify this expression:

\(\frac{6^7 \cdot 6^4}{2^6 \cdot 2^{-1}}\)

Let’s break it down using what we just learned.

• In the numerator, you’re multiplying powers with the same base:
  6⁷ × 6⁴ = 6¹¹
• In the denominator, you’re also multiplying powers with the same base:
  2⁶ × 2⁻¹ = 2⁵

So the simplified expression becomes:

\(\frac{6^{11}}{2^5}\)

And that’s your final answer—fully simplified with only positive exponents.

Final Tip

Once you’re comfortable with these exponent rules, you’ll be able to simplify even tricky-looking expressions quickly. Practice a few more like this, and you’ll be ready for anything the GED throws at you!

Last Updated on October 20, 2025.