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.
Simplify a^2 · a^6.
- 2.
Evaluate (−2)^3.
- 3.
Evaluate 5^0.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify (2³)² · 2⁴.
- 2.
Simplify (−3)³ · (−3)² ÷ (−3)⁴.