Solve \(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)
A
\(\frac{3}{2}\)
B
\(\frac{1}{2}\)
C
\(\frac{1}{3}\)
D
\(\frac{5}{3}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)
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 = \(\frac{2}{4}\) = \(\frac{1}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #69048)