Discussion

If \(2^x \times 16^{\frac{2}{5}} = 2^{\frac{1}{5}}\), then \(x\) is equal to:

Answer: D

\(2^x \times 16^{\frac{2}{5}} = 2^{\frac{1}{5}}\)

\(\Rightarrow 2^x \times (2^4)^{\frac{2}{5}} = 2^{\frac{1}{5}} \)

\(\Rightarrow 2^x \times 2^{\frac{8}{5}}= 2^{\frac{1}{5}} \)

\(\Rightarrow 2^{(x+ \frac{8}{5})} = 2^{\frac{1}{5}} \)

\(\Rightarrow x + \frac{8}{5} = \frac{1}{5} \)

\(\Rightarrow x = (\frac{1}{5} - \frac{8}{5}) = -\frac{7}{5}\)

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