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

Mathematics
WAEC 2023

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

  • A. \(\frac{3}{2}\)
  • B. \(\frac{1}{2}\)
  • C. \(\frac{1}{3}\)
  • D. \(\frac{5}{3}\)
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Correct Answer: Option B
Explanation

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

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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