Simplify ((6x)^2)/((4x^2)^3)

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

Simplify the numerator.

Apply the product rule to $6 x$ .

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

Raise $6$ to the power of $2$ .

$\frac{36 x^{2}}{{(4 x^{2})}^{3}}$

Simplify the denominator.

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

$\frac{36 x^{2}}{4^{3} {(x^{2})}^{3}}$

Raise $4$ to the power of $3$ .

$\frac{36 x^{2}}{64 {(x^{2})}^{3}}$

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

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

$\frac{36 x^{2}}{64 x^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{36 x^{2}}{64 x^{6}}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $36$ and $64$ .

Factor $4$ out of $36 x^{2}$ .

$\frac{4 (9 x^{2})}{64 x^{6}}$

Cancel the common factors.

Factor $4$ out of $64 x^{6}$ .

$\frac{4 (9 x^{2})}{4 (16 x^{6})}$

Cancel the common factor.

$\frac{4 (9 x^{2})}{4 (16 x^{6})}$

Rewrite the expression.

$\frac{9 x^{2}}{16 x^{6}}$

Cancel the common factor of $x^{2}$ and $x^{6}$ .

Factor $x^{2}$ out of $9 x^{2}$ .

$\frac{x^{2} \cdot 9}{16 x^{6}}$

Cancel the common factors.

Factor $x^{2}$ out of $16 x^{6}$ .

$\frac{x^{2} \cdot 9}{x^{2} (16 x^{4})}$

Cancel the common factor.

$\frac{x^{2} \cdot 9}{x^{2} (16 x^{4})}$

Rewrite the expression.

$\frac{9}{16 x^{4}}$