Question 9.

If x = (4096)^{7+4√3}, then which of the following equals 64?

A

\frac{x^{7/2}}{x^{4/√3}}

B

\frac{x^{7}}{x^{4√3}}

C

\frac{x^{7/2}}{x^{2√3}}

D

\frac{x^{7}}{x^{2√3}}

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Text Explanation

$x = 2^{12(7 + 4\sqrt3)}$

$x^{7/2} = 2^{42(7 + 4\sqrt3)}$

$x^{2\sqrt3} = 2^{24\sqrt3(7 + 4\sqrt3)}$

$\frac{x^{7/2}}{x^{2\sqrt3}} = 2^{(7 + 4\sqrt3)(42 - 24\sqrt3)} = 2^{(7 + 4\sqrt3)(7 - 4\sqrt3)6} = 2^6$

Hence correct option is C.

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