Bunuel wrote:
If x > 0, what is the value of x^5 ?
(1) \(\sqrt{x}=32\)
(2) x^2 = 2^20
We are given that x is greater than zero and need to determine the value of x^5.
Statement One Alone:√x = 32
Using the equation in statement one, we can determine a value of x.
√x = 32
(√x)^2 = 32^2
x = 32^2 = (2^5)^2 = 2^10
Since x = 2^10, x^5 = (2^10)^5 = 2^50
Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.
Statement Two Alone:x^2 = 2^20
Using the equation in statement two, we can determine a value of x.
√(x^2) = +/-√(2^20)
x = +/-2^10
Since x is positive, x = 2^10.
Since x = 2^10, x^5 = (2^10)^5 = 2^50.
Answer: D
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