Grade 8 Exponents: Unit Review

Worked examples

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

1. Example 1

   2⁵ ÷ 2⁴ = 2ⁿ. What is n?

   1. Same base, dividing: subtract the exponents: 5 − 4 = 1.
   2. So 2⁵ ÷ 2⁴ = 2¹, which means n = 1.

   Answer: 1

2. Example 2

   (11⁵)² × 11⁵ = 11ⁿ. What is n?

   1. Power of a power: multiply the exponents. (11⁵)² = 11¹⁰ (5 × 2 = 10).
   2. Same base, multiplying: add the exponents: 10 + 5 = 15.
   3. So (11⁵)² × 11⁵ = 11¹⁵, which means n = 15.

   Answer: 15

3. Example 3

   Find the value of 5⁻⁴. Write your answer as a fraction.

   1. A negative exponent means "one over": 5⁻⁴ = 1/5⁴.
   2. 5⁴ = 5 × 5 × 5 × 5 = 625, so the value is 1/625.

   Answer: 1/625