Simplify the expression. \[ \left(z^{\frac{1}{5}} \cdot y^{-\frac{5}{3}}\right)^{3} \]

Step 1 ：Distribute the exponent of 3 to each term inside the parentheses: \(\left(z^{\frac{1}{5}}\right)^{3} \cdot \left(y^{-\frac{5}{3}}\right)^{3}\)

Step 2 ：Raise a power to a power by multiplying the exponents: \(z^{\frac{3}{5}} \cdot y^{-\frac{15}{3}}\)

Step 3 ：Simplify -15/3 to -5: \(z^{\frac{3}{5}} \cdot y^{-5}\)

Step 4 ：\(\boxed{z^{\frac{3}{5}} \cdot y^{-5}}\) is the final simplified expression