Grade 8 Exponents: Negative Exponents

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   (8⁻⁶)⁻² = 8ⁿ. What is n?

   1. Power of a power: multiply the exponents. (8⁻⁶)⁻² = 8¹² (−6 × (−2) = 12).
   2. So (8⁻⁶)⁻² = 8¹², which means n = 12.

   Answer: 12

2. Example 2

   Find the value of 8⁶ × 8⁻⁹. Write your answer as a fraction.

   1. Same base, multiplying: add the exponents: 6 + (−9) = −3.
   2. A negative exponent means "one over": 8⁻³ = 1/8³.
   3. 8³ = 8 × 8 × 8 = 512, so the value is 1/512.

   Answer: 1/512

3. Example 3

   Find the value of 4⁴ × 4⁻⁷. Write your answer as a fraction.

   1. Same base, multiplying: add the exponents: 4 + (−7) = −3.
   2. A negative exponent means "one over": 4⁻³ = 1/4³.
   3. 4³ = 4 × 4 × 4 = 64, so the value is 1/64.

   Answer: 1/64