Graduate Management Admission Test (GMAT) Practice Test

Disable ads (and more) with a membership for a one time $2.99 payment

Study for the Graduate Management Admission Test (GMAT) with multiple-choice questions and detailed explanations. Enhance your preparation with practice flashcards and hints. Get ready for your GMAT exam!

Each practice test/flash card set has 50 randomly selected questions from a bank of over 500. You'll get a new set of questions each time!

Practice this question and more.

What is 27⁴ʹ³ simplified to in terms of a cube root?

³√(27²)
³√(27⁴) = (³√27)²
³√(27⁴) = (³√27)⁴ = 3⁴ = 81
81

The correct answer is: ³√(27⁴) = (³√27)⁴ = 3⁴ = 81

To understand why the choice is correct, it is essential to break down the expression 27⁴ʹ³ in terms of cube roots. Start by recalling that 27 can be expressed as 3³, which means that 27⁴ can be rewritten in its prime factor form: 27⁴ = (3³)⁴ = 3¹². Now, when we simplify 27⁴ under a cube root, we can use the property of roots: ³√(27⁴) can be rewritten as ³√(3¹²). Utilizing the property of exponents, we divide the exponent by the root: ³√(3¹²) = 3^(12/3) = 3⁴. Recognizing that 3⁴ equals 81 confirms that the expression ³√(27⁴) simplifies to 81. This step-by-step process is why this choice is the correct option. It accurately reflects the logarithmic and exponential relationships involved in dealing with cube roots and powers. The answer correctly arrives at 81 through its acknowledgment of the cube root’s properties and the arithmetic involved with exponents.