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WAEC Mathematics 2023 Paper

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Question : 14

Total: 50

Solve

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

$\;\frac{3}{2}$
$\;\frac{1}{2}$
$\;\frac{1}{3}$
$\;\frac{5}{3}$

Solution:

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

applying the laws of indices

$2^{5x - x} = 2^{10\left(\frac{1}{5}\right)}$

$2^{4x} = 2^{10\left(\frac{1}{5}\right)}$

$2^{4x} = 2^2$

Equating the powers

then 4x = 2

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

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