Simplify (-3x^5y^(1/3))^3

${(- 3 x^{5} y^{\frac{1}{3}})}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- 3 x^{5} y^{\frac{1}{3}}$ .

${(- 3 x^{5})}^{3} {(y^{\frac{1}{3}})}^{3}$

Apply the product rule to $- 3 x^{5}$ .

${(- 3)}^{3} {(x^{5})}^{3} {(y^{\frac{1}{3}})}^{3}$

Raise $- 3$ to the power of $3$ .

$- 27 {(x^{5})}^{3} {(y^{\frac{1}{3}})}^{3}$

Multiply the exponents in ${(x^{5})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 27 x^{5 \cdot 3} {(y^{\frac{1}{3}})}^{3}$

Multiply $5$ by $3$ .

$- 27 x^{15} {(y^{\frac{1}{3}})}^{3}$

Multiply the exponents in ${(y^{\frac{1}{3}})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 27 x^{15} y^{\frac{1}{3} \cdot 3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 27 x^{15} y^{\frac{1}{3} \cdot 3}$

Rewrite the expression.

$- 27 x^{15} y^{1}$

Simplify.

$- 27 x^{15} y$