Compare 32 to the 4th power with 16 to the 5th

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Quantitative Reasoning

Quantity A: $32^{4}$ Quantity B: $16^{5}$

Compare Quantity A and Quantity B. Select one answer.

AQuantity A is greater.BQuantity B is greater.CThe two quantities are equal.DThe relationship cannot be determined from the information given.

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Answer: C (The two quantities are equal.)

Express both quantities as powers of 2. Since $32 = 2^{5}$ , Quantity A is $(2^{5})^{4} = 2^{20}$ . Since $16 = 2^{4}$ , Quantity B is $(2^{4})^{5} = 2^{20}$ . Therefore, the two quantities are equal.

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Quantitative Reasoning

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