Addition and Subtraction

4-1Exponents

Overview

An exponent shows repeated multiplication: a^n = a · a · … · a (n factors).

Key ideas

  • Product rule: a^m · a^n = a^(m+n).
  • a^1 = a; a^0 = 1 (a ≠ 0).
  • Be careful: −3^2 = −9 but (−3)^2 = 9.

Worked examples

Example 1

Problem. Simplify x^3 · x^4.

Solution. x^7

Example 2

Problem. Evaluate 2^5.

Solution. 32

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Simplify a^2 · a^6.

  2. 2.

    Evaluate (−2)^3.

  3. 3.

    Evaluate 5^0.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Simplify (2³)² · 2⁴.

  2. 2.

    Simplify (−3)³ · (−3)² ÷ (−3)⁴.