If \(2^x \times 16^{\frac{2}{5}} = 2^{\frac{1}{5}}\), then \(x\) is equal to:
Answer: D
\(2^x \times 16^{\frac{2}{5}} = 2^{\frac{1}{5}}\)
\(\Rightarrow 2^x \times (2^4)^{\frac{2}{5}} = 2^{\frac{1}{5}} \)
\(\Rightarrow 2^x \times 2^{\frac{8}{5}}= 2^{\frac{1}{5}} \)
\(\Rightarrow 2^{(x+ \frac{8}{5})} = 2^{\frac{1}{5}} \)
\(\Rightarrow x + \frac{8}{5} = \frac{1}{5} \)
\(\Rightarrow x = (\frac{1}{5} - \frac{8}{5}) = -\frac{7}{5}\)