Simplify (3^3-3^2)/((3/4)^2)

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

Step 1

Simplify the numerator.

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

$\frac{27 - 3^{2}}{{(\frac{3}{4})}^{2}}$

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

$\frac{27 - 1 \cdot 9}{{(\frac{3}{4})}^{2}}$

Multiply $- 1$ by $9$ .

$\frac{27 - 9}{{(\frac{3}{4})}^{2}}$

Subtract $9$ from $27$ .

$\frac{18}{{(\frac{3}{4})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $\frac{3}{4}$ .

$\frac{18}{\frac{3^{2}}{4^{2}}}$

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

$\frac{18}{\frac{9}{4^{2}}}$

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

$\frac{18}{\frac{9}{16}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$18 (\frac{16}{9})$

Step 4

Cancel the common factor of $9$ .

Factor $9$ out of $18$ .

$9 (2) \frac{16}{9}$

Cancel the common factor.

$9 \cdot 2 \frac{16}{9}$

Rewrite the expression.

$2 \cdot 16$

Step 5

Multiply $2$ by $16$ .

$32$