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Solve $2^{5x} \div 2^x = \sqrt[5]{2^{10}}$ ...

Solve $2^{5x} \div 2^x = \sqrt[5]{2^{10}}$

A.

$\frac{3}{2}$

B.

$\frac{1}{2}$

C.

$\frac{1}{3}$

D.

$\frac{5}{3}$

View answer & explanation

Correct answer is B

$2^{5x} \div 2^x = \sqrt[5]{2^{10}}$

applying the laws of indices

$2^{5x - x} = 2^{10(1/5)}$

$2^{4x} = 2^{10(1/5)}$

$2^{4x} = 2^2$
Equating the powers
then 4x = 2

therefore, x = $\frac{2}{4}$ = $\frac{1}{2}$

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