Simplify ((x^18)/(y^-6))^(2/3)

${(\frac{x^{18}}{y^{- 6}})}^{\frac{2}{3}}$

Step 1

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

${(x^{18} y^{6})}^{\frac{2}{3}}$

Step 2

Apply the product rule to $x^{18} y^{6}$ .

${(x^{18})}^{\frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Step 3

Multiply the exponents in ${(x^{18})}^{\frac{2}{3}}$ .

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

$x^{18 (\frac{2}{3})} {(y^{6})}^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $18$ .

$x^{3 (6) \frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Cancel the common factor.

$x^{3 \cdot 6 \frac{2}{3}} {(y^{6})}^{\frac{2}{3}}$

Rewrite the expression.

$x^{6 \cdot 2} {(y^{6})}^{\frac{2}{3}}$

Multiply $6$ by $2$ .

$x^{12} {(y^{6})}^{\frac{2}{3}}$

Step 4

Multiply the exponents in ${(y^{6})}^{\frac{2}{3}}$ .

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

$x^{12} y^{6 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$x^{12} y^{3 (2) \frac{2}{3}}$

Cancel the common factor.

$x^{12} y^{3 \cdot 2 \frac{2}{3}}$

Rewrite the expression.

$x^{12} y^{2 \cdot 2}$

Multiply $2$ by $2$ .

$x^{12} y^{4}$