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\({a^{\frac{m}{n}} = \sqrt[n]{a}^m}\)

Simplify \(16^{\frac{3}{2}}\)

\(=(\sqrt{16})^{3}\)

\(=4^{3}\)

\(=64\)

Simplify \(32^{\frac{3}{5}}\)

=\((\sqrt[5]{32})^{3}\)

\(= 2^{3}\)

\(=8\)

Simplify \(8^{\frac{-2}{3}}\)

\(=(\sqrt[3]{8})^{-2}\)

\(=2^{-2}\)

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

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

Simplify \(y^{\frac{-3}{4}}\times y^{\frac{1}{4}}\)

Add the indices \(\frac{-3}{4}+\frac{1}{4}=\frac{-2}{4}\) which simplifies to \(\frac{-1}{2}\)

\(= y^{\frac{-1}{2}}\)