Simplify the expression.
${(z^{\frac{1}{5}} \cdot y^{- \frac{5}{3}})}^{3}$

Answer

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Answer

$z^{\frac{3}{5}} \cdot y^{- 5}$ is the final simplified expression

Steps

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

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 ： $z^{\frac{3}{5}} \cdot y^{- 5}$ is the final simplified expression