Simplify ((s^3t)/(st^4))^2

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

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

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

${(\frac{s (s^{2} t)}{s t^{4}})}^{2}$

Cancel the common factors.

Factor $s$ out of $s t^{4}$ .

${(\frac{s (s^{2} t)}{s (t^{4})})}^{2}$

Cancel the common factor.

${(\frac{s (s^{2} t)}{s t^{4}})}^{2}$

Rewrite the expression.

${(\frac{s^{2} t}{t^{4}})}^{2}$

Cancel the common factor of $t$ and $t^{4}$ .

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

${(\frac{t s^{2}}{t^{4}})}^{2}$

Cancel the common factors.

Factor $t$ out of $t^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Apply basic rules of exponents.

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

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

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

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

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

Multiply $2$ by $2$ .

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

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

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

$\frac{s^{4}}{t^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{s^{4}}{t^{6}}$