Simplify ((3x^9)/(y^3))^-5

${(\frac{3 x^{9}}{y^{3}})}^{- 5}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{y^{3}}{3 x^{9}})}^{5}$

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

Apply the product rule to $\frac{y^{3}}{3 x^{9}}$ .

$\frac{{(y^{3})}^{5}}{{(3 x^{9})}^{5}}$

Apply the product rule to $3 x^{9}$ .

$\frac{{(y^{3})}^{5}}{3^{5} {(x^{9})}^{5}}$

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

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

$\frac{y^{3 \cdot 5}}{3^{5} {(x^{9})}^{5}}$

Multiply $3$ by $5$ .

$\frac{y^{15}}{3^{5} {(x^{9})}^{5}}$

Simplify the denominator.

Raise $3$ to the power of $5$ .

$\frac{y^{15}}{243 {(x^{9})}^{5}}$

Multiply the exponents in ${(x^{9})}^{5}$ .

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

$\frac{y^{15}}{243 x^{9 \cdot 5}}$

Multiply $9$ by $5$ .

$\frac{y^{15}}{243 x^{45}}$