Problems Involving Exponents
7-9Negative Exponents
Overview
a^(−n) = 1/a^n (a ≠ 0). Negative exponents represent reciprocals.
Key ideas
- Move a factor from numerator to denominator (or back) to change the sign of its exponent.
- Rules for exponents still apply.
- Final answers usually have only positive exponents.
Worked examples
Example 1
Problem. Simplify 2^(−3).
Solution. 1/2^3 = 1/8
Example 2
Problem. Simplify x^(−2) · x^5.
Solution. x^3
Practice
Try each one. Click Show answer when ready.
- 1.
Simplify 5^(−2).
- 2.
Simplify (x^4)·(x^(−6)).
- 3.
Simplify (a^(−3))/(a^(−5)).
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify (2x⁻³y²)/(x²y⁻⁴).
- 2.
Simplify (3a²b⁻³)⁻².