CMClearMathAcademy

Exponents and Radical Foundations

A free College Algebra lesson from the “Exponents and Radicals” unit, with a worked example and practice problems including step-by-step solutions.

Exponent rules organize repeated multiplication. When multiplying same bases, add exponents; when raising a power to a power, multiply exponents.

What you'll learn

Why it matters: Scaling laws, scientific formulas, compound units, and repeated growth all use exponents to compress multiplication. The rules are not shortcuts to memorize; they describe how repeated factors are grouped.

Worked example

Problem. Simplify (x^3)^4.

  1. Use the power-to-power rule.
  2. Multiply 3 and 4.
  3. The result is x^12.

Answer: x^12

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Simplify x^4 times x^5.

Show solution
  1. Add exponents.

Answer: x^9

2. Simplify (a^2)^6.

Show solution
  1. Multiply exponents.

Answer: a^12

3. Simplify b^0 for b not equal to 0.

Show solution
  1. Any nonzero base to the zero power is 1.

Answer: 1

4. Simplify x^5 * x^2.

Choices: x^7 · x^10 · x^3 · 2x^7

Show solution
  1. Add exponents with the same base.

Answer: x^7

5. Simplify (a^3)^4.

Choices: a^12 · a^7 · a^1 · 4a^3

Show solution
  1. Multiply the exponents.

Answer: a^12

Practice this interactively with instant feedback and an AI tutor.

Practice Exponents and Radical Foundations Take the free placement check

More College Algebra lessons