Simplify ((3c)/(4a^2bc^2))^2

${(\frac{3 c}{4 a^{2} b c^{2}})}^{2}$

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

Factor $c$ out of $3 c$ .

${(\frac{c \cdot 3}{4 a^{2} b c^{2}})}^{2}$

Cancel the common factors.

Factor $c$ out of $4 a^{2} b c^{2}$ .

${(\frac{c \cdot 3}{c (4 a^{2} b c)})}^{2}$

Cancel the common factor.

${(\frac{c \cdot 3}{c (4 a^{2} b c)})}^{2}$

Rewrite the expression.

${(\frac{3}{4 a^{2} b c})}^{2}$

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

Apply the product rule to $\frac{3}{4 a^{2} b c}$ .

$\frac{3^{2}}{{(4 a^{2} b c)}^{2}}$

Apply the product rule to $4 a^{2} b c$ .

$\frac{3^{2}}{{(4 a^{2} b)}^{2} c^{2}}$

Apply the product rule to $4 a^{2} b$ .

$\frac{3^{2}}{{(4 a^{2})}^{2} b^{2} c^{2}}$

Apply the product rule to $4 a^{2}$ .

$\frac{3^{2}}{4^{2} {(a^{2})}^{2} b^{2} c^{2}}$

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

$\frac{9}{4^{2} {(a^{2})}^{2} b^{2} c^{2}}$

Simplify the denominator.

Raise $4$ to the power of $2$ .

$\frac{9}{16 {(a^{2})}^{2} b^{2} c^{2}}$

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

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

$\frac{9}{16 a^{2 \cdot 2} b^{2} c^{2}}$

Multiply $2$ by $2$ .

$\frac{9}{16 a^{4} b^{2} c^{2}}$