Simplify (3z)^2(6z^2)^-3

${(3 z)}^{2} {(6 z^{2})}^{- 3}$

Apply the product rule to $3 z$ .

$3^{2} z^{2} {(6 z^{2})}^{- 3}$

Raise $3$ to the power of $2$ .

$9 z^{2} {(6 z^{2})}^{- 3}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$9 z^{2} \frac{1}{{(6 z^{2})}^{3}}$

Simplify the denominator.

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Apply the product rule to $6 z^{2}$ .

$9 z^{2} \frac{1}{6^{3} {(z^{2})}^{3}}$

Raise $6$ to the power of $3$ .

$9 z^{2} \frac{1}{216 {(z^{2})}^{3}}$

Multiply the exponents in ${(z^{2})}^{3}$ .

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

$9 z^{2} \frac{1}{216 z^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$9 z^{2} \frac{1}{216 z^{6}}$

Cancel the common factor of $9 z^{2}$ .

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Factor $9 z^{2}$ out of $216 z^{6}$ .

$9 z^{2} \frac{1}{9 z^{2} (24 z^{4})}$

Cancel the common factor.

$9 z^{2} \frac{1}{9 z^{2} (24 z^{4})}$

Rewrite the expression.

$\frac{1}{24 z^{4}}$

Simplify (3z)^2(6z^2)^-3