Simplify (-8x^5y^3)^(1/3)

${(- 8 x^{5} y^{3})}^{\frac{1}{3}}$

Step 1

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

Apply the product rule to $- 8 x^{5} y^{3}$ .

${(- 8 x^{5})}^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}}$

Apply the product rule to $- 8 x^{5}$ .

${(- 8)}^{\frac{1}{3}} {(x^{5})}^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}}$

Step 2

Simplify the expression.

Rewrite $- 8$ as ${(- 2)}^{3}$ .

${({(- 2)}^{3})}^{\frac{1}{3}} {(x^{5})}^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}}$

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

${(- 2)}^{3 (\frac{1}{3})} {(x^{5})}^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 2)}^{3 (\frac{1}{3})} {(x^{5})}^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}}$

Rewrite the expression.

${(- 2)}^{1} {(x^{5})}^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}}$

Step 4

Simplify the expression.

Evaluate the exponent.

$- 2 {(x^{5})}^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}}$

Multiply the exponents in ${(x^{5})}^{\frac{1}{3}}$ .

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

$- 2 x^{5 (\frac{1}{3})} {(y^{3})}^{\frac{1}{3}}$

Combine $5$ and $\frac{1}{3}$ .

$- 2 x^{\frac{5}{3}} {(y^{3})}^{\frac{1}{3}}$

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

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

$- 2 x^{\frac{5}{3}} y^{3 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 2 x^{\frac{5}{3}} y^{3 (\frac{1}{3})}$

Rewrite the expression.

$- 2 x^{\frac{5}{3}} y^{1}$

Step 5

Simplify.

$- 2 x^{\frac{5}{3}} y$

Step 6

Reorder factors in $- 2 x^{\frac{5}{3}} y$ .

$- 2 y x^{\frac{5}{3}}$