Simplify ((x^3)/(y^-6))^(1/3)

${(\frac{x^{3}}{y^{- 6}})}^{\frac{1}{3}}$

Step 1

Move $y^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(x^{3} y^{6})}^{\frac{1}{3}}$

Step 2

Apply the product rule to $x^{3} y^{6}$ .

${(x^{3})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

Step 3

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

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

$x^{3 (\frac{1}{3})} {(y^{6})}^{\frac{1}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$x^{3 (\frac{1}{3})} {(y^{6})}^{\frac{1}{3}}$

Rewrite the expression.

$x^{1} {(y^{6})}^{\frac{1}{3}}$

Step 4

Simplify.

$x {(y^{6})}^{\frac{1}{3}}$

Step 5

Multiply the exponents in ${(y^{6})}^{\frac{1}{3}}$ .

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

$x y^{6 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

$x y^{3 \cdot 2 \frac{1}{3}}$

Rewrite the expression.

$x y^{2}$