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Video: Using the Power of a Power Rule to Identify Equivalent Expressions

Kathryn Kingham

Which of the following is equal to [(3²)⁴]⁵? [A] 3¹²⁰ [B] 3¹⁸ [C] 3⁴⁰ [D] 3¹¹ [E] 3³⁰

01:10

Video Transcript

Which of the following is equal to three squared to the fourth power to the fifth power? A) three to the 120th power, B) three to the 18th power, C) three to the 40th power, D) three to the 11th power, or E) three to the 30th power.

To solve this question, we’ll need to know how to take a power of a power. To raise a power to a power, you need to multiply the exponents together. We’re raising three squared to the fourth power, and then we’re taking whenever we get there and raising it to the fifth power.

This means that we’ll need to multiply all three of our exponents together, two times four times five. Three squared to the fourth power to the fifth power is going to be equal to three to the 40th power.