Exponents Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Exponents.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

An operation representing repeated multiplication: a^n means a multiplied by itself n times.

2^3 means 2 \times 2 \times 2 = 8. The exponent tells you how many times to multiply.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Exponents compress repeated multiplication into compact notation.

Common stuck point: Negative and fractional exponents extend the pattern in non-obvious ways.

Sense of Study hint: Write out the repeated multiplication fully before computing, e.g., write 2 x 2 x 2 instead of jumping to the answer.

Worked Examples

Example 1

easy
Compute 5^3.

Solution

  1. 1
    Recognize that the exponent 3 means multiply the base 5 by itself three times.
  2. 2
    Write the base 5 multiplied by itself 3 times: 5 \times 5 \times 5.
  3. 3
    Compute step by step: 5 \times 5 = 25, then 25 \times 5 = 125.

Answer

125
An exponent tells you how many times to multiply the base by itself. Here 5^3 means three factors of 5.

Example 2

medium
Simplify (-2)^4.

Example 3

medium
Simplify \frac{2^5 \times 2^3}{2^4}.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Compute 2^6.

Example 2

medium
Which is larger, 3^4 or 4^3? Compute both to compare.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

multiplication