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. \(\frac{5}{3}\)
Correct Answer: B. \(\frac{1}{2}\)
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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