Simplify ((2x)^-2)/((3x)^-2)

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

Step 1

Simplify the expression.

Move ${(2 x)}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(3 x)}^{- 2} {(2 x)}^{2}}$

Move ${(3 x)}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the numerator.

Apply the product rule to $3 x$ .

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

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

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

Step 3

Simplify the denominator.

Apply the product rule to $2 x$ .

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

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

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

Step 4

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{9}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$