Write the logarithmic equation in exponential form. For example, the exponential form of \( \log _{5}(25)=2 \) is \( 5^{2}= \) \[ \log _{32}(4)=\frac{2}{5} \]

To rewrite the logarithmic equation \(\log_{32}(4) = \frac{2}{5}\) in exponential form, we can apply the definition of a logarithm. This means that if \(\log_b(a) = c\), then it can be rewritten as \(b^c = a\). So, transforming \(\log_{32}(4) = \frac{2}{5}\) into exponential form gives us: \[ 32^{\frac{2}{5}} = 4. \] This equation tells us that raising 32 to the power of \(\frac{2}{5}\) will yield 4!