Solve: \(\frac{2^{5x}}{2^x} = \sqrt[5]{2^{20}}\)
Solution
\[ \frac{2^{5x}}{2^x} = \sqrt[5]{2^{20}} \]
\[ = 2^{5x-x} = (2^{20})^{1/5} \]
\[ = 2^{4x} = 2^4 \]
\[ \Rightarrow 4x = 4 \]
\[ \Rightarrow x = 1 \]
Final Answer:
\[ \boxed{x = 1} \]
\[ \frac{2^{5x}}{2^x} = \sqrt[5]{2^{20}} \]
\[ = 2^{5x-x} = (2^{20})^{1/5} \]
\[ = 2^{4x} = 2^4 \]
\[ \Rightarrow 4x = 4 \]
\[ \Rightarrow x = 1 \]
\[ \boxed{x = 1} \]