Simplify ((x^(-2/3))/(y^(-1/3)))^15

${(\frac{x^{- \frac{2}{3}}}{y^{- \frac{1}{3}}})}^{15}$

Step 1

Move $x^{- \frac{2}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{y^{- \frac{1}{3}} x^{\frac{2}{3}}})}^{15}$

Step 2

Move $y^{- \frac{1}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{y^{\frac{1}{3}}}{x^{\frac{2}{3}}})}^{15}$

Step 3

Apply the product rule to $\frac{y^{\frac{1}{3}}}{x^{\frac{2}{3}}}$ .

$\frac{{(y^{\frac{1}{3}})}^{15}}{{(x^{\frac{2}{3}})}^{15}}$

Step 4

Multiply the exponents in ${(y^{\frac{1}{3}})}^{15}$ .

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

$\frac{y^{\frac{1}{3} \cdot 15}}{{(x^{\frac{2}{3}})}^{15}}$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$\frac{y^{\frac{1}{3} \cdot (3 (5))}}{{(x^{\frac{2}{3}})}^{15}}$

Cancel the common factor.

$\frac{y^{\frac{1}{3} \cdot (3 \cdot 5)}}{{(x^{\frac{2}{3}})}^{15}}$

Rewrite the expression.

$\frac{y^{5}}{{(x^{\frac{2}{3}})}^{15}}$

Step 5

Multiply the exponents in ${(x^{\frac{2}{3}})}^{15}$ .

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

$\frac{y^{5}}{x^{\frac{2}{3} \cdot 15}}$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{y^{5}}{x^{2 \cdot 5}}$

Multiply $2$ by $5$ .

$\frac{y^{5}}{x^{10}}$