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

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

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

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

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

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

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

Simplify the numerator.

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

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

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

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

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

Multiply $3$ by $2$ .

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

Simplify terms.

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

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

Combine.

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

Cancel the common factor of $s^{3}$ and $s^{2}$ .

Factor $s^{2}$ out of $4 r^{6} s^{3}$ .

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

Cancel the common factors.

Factor $s^{2}$ out of $s^{2} {(r^{3})}^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Multiply $3$ by $3$ .

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

Cancel the common factor of $r^{6}$ and $r^{9}$ .

Factor $r^{6}$ out of $4 r^{6} s$ .

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

Cancel the common factors.

Factor $r^{6}$ out of $r^{9}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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