Simplify (r^-2s^3)^2(3s)^2

${(r^{- 2} s^{3})}^{2} {(3 s)}^{2}$

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

${(\frac{1}{r^{2}} s^{3})}^{2} {(3 s)}^{2}$

Combine $\frac{1}{r^{2}}$ and $s^{3}$ .

${(\frac{s^{3}}{r^{2}})}^{2} {(3 s)}^{2}$

Simplify the expression.

Apply the product rule to $\frac{s^{3}}{r^{2}}$ .

$\frac{{(s^{3})}^{2}}{{(r^{2})}^{2}} {(3 s)}^{2}$

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

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

$\frac{s^{3 \cdot 2}}{{(r^{2})}^{2}} {(3 s)}^{2}$

Multiply $3$ by $2$ .

$\frac{s^{6}}{{(r^{2})}^{2}} {(3 s)}^{2}$

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

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

$\frac{s^{6}}{r^{2 \cdot 2}} {(3 s)}^{2}$

Multiply $2$ by $2$ .

$\frac{s^{6}}{r^{4}} {(3 s)}^{2}$

Apply the product rule to $3 s$ .

$\frac{s^{6}}{r^{4}} (3^{2} s^{2})$

Rewrite using the commutative property of multiplication.

$3^{2} \frac{s^{6}}{r^{4}} s^{2}$

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

$9 \frac{s^{6}}{r^{4}} s^{2}$

Combine $9$ and $\frac{s^{6}}{r^{4}}$ .

$\frac{9 s^{6}}{r^{4}} s^{2}$

Multiply $\frac{9 s^{6}}{r^{4}} s^{2}$ .

Combine $\frac{9 s^{6}}{r^{4}}$ and $s^{2}$ .

$\frac{9 s^{6} s^{2}}{r^{4}}$

Multiply $s^{6}$ by $s^{2}$ by adding the exponents.

Move $s^{2}$ .

$\frac{9 (s^{2} s^{6})}{r^{4}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 s^{2 + 6}}{r^{4}}$

Add $2$ and $6$ .

$\frac{9 s^{8}}{r^{4}}$