Evaluate (4(3x)^2)/((2x)^2)

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

Step 1

Simplify the numerator.

Apply the product rule to $3 x$ .

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

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

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

Multiply $4$ by $9$ .

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

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

Step 2

Simplify the denominator.

Apply the product rule to $2 x$ .

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

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

$\frac{36 x^{2}}{4 x^{2}}$

$\frac{36 x^{2}}{4 x^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $36$ and $4$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factor.

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

Divide $9$ by $1$ .

$9$

$9$

$9$

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