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

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

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

Factor $r$ out of $r^{2} s$ .

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

Cancel the common factors.

Factor $r$ out of $r s^{3} t$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $s$ out of $r s$ .

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

Cancel the common factors.

Factor $s$ out of $s^{3} t$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Apply the product rule to $s^{2} t$ .

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

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

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

$\frac{r^{3}}{s^{2 \cdot 3} t^{3}}$

Multiply $2$ by $3$ .

$\frac{r^{3}}{s^{6} t^{3}}$