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

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

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

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Apply the product rule to $\frac{3}{5 y^{9}}$ .

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

Apply the product rule to $5 y^{9}$ .

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

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

$\frac{27}{5^{3} {(y^{9})}^{3}}$

Simplify the denominator.

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

$\frac{27}{125 {(y^{9})}^{3}}$

Multiply the exponents in ${(y^{9})}^{3}$ .

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

$\frac{27}{125 y^{9 \cdot 3}}$

Multiply $9$ by $3$ .

$\frac{27}{125 y^{27}}$

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

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