Grade 8 Exponents: Power Rule

Worked examples

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

1. Example 1

   (pⁿ)³ = p²⁴. What is n?

   1. Power of a power: multiply the exponents. (pⁿ)³ = p³ⁿ.
   2. The exponents on both sides must be equal: 3n = 24.
   3. So n = 24 ÷ 3 = 8.

   Answer: 8

2. Example 2

   (4ⁿ)⁴ = 4¹². What is n?

   1. Power of a power: multiply the exponents. (4ⁿ)⁴ = 4⁴ⁿ.
   2. The exponents on both sides must be equal: 4n = 12.
   3. So n = 12 ÷ 4 = 3.

   Answer: 3

3. Example 3

   (10ⁿ)² = 10¹⁰. What is n?

   1. Power of a power: multiply the exponents. (10ⁿ)² = 10²ⁿ.
   2. The exponents on both sides must be equal: 2n = 10.
   3. So n = 10 ÷ 2 = 5.

   Answer: 5