SAT Math Multiple Choice Question 725: Answer and Explanation

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Question: 725

5. If y3 = 20 and z2 = 10, what is the value of (yz)6?

  • A. 2 × 105
  • B. 4 × 104
  • C. 2 × 105
  • D. 4 × 105

Correct Answer: D

Explanation:

D

Algebra (exponentials) EASY

Although solving for y and z isn't hard, it is even simpler to just express (yz)6 in terms of y3 and z2, using the Laws of Exponentials from Chapter 9, Lesson 9.

Original expression:

(yz)6

Law of Exponentials #5:

y6 z6

Law of Exponentials #8:

(y3)2(z2)3

Substitute y3 = 20 and z2 = 10:

(20)2(10)3

Substitute 20 = (2)(10):

(2)2(10)2(10)3

Combine terms with like bases with Law of Exponents #4:

22(10)5

Simplify:

4 × 105

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