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 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 = \(\frac{2}{4}\) = \(\frac{1}{2}\)
