Questions: Simplify: (3^3-3^2)/((3/4)^2).

Transcript text: Simplify: $\frac{3^{3}-3^{2}}{\left(\frac{3}{4}\right)^{2}}$.

Solution

Step 1: Simplify the Numerator

The numerator of the expression is $3^3 - 3^2$.

Calculate $3^3$: \[ 3^3 = 27 \]

Calculate $3^2$: \[ 3^2 = 9 \]

Subtract the two results: \[ 27 - 9 = 18 \]

Step 2: Simplify the Denominator

The denominator of the expression is $\left(\frac{3}{4}\right)^2$.

Calculate $\left(\frac{3}{4}\right)^2$: \[ \left(\frac{3}{4}\right)^2 = \frac{3^2}{4^2} = \frac{9}{16} \]

Step 3: Divide the Numerator by the Denominator

Now, divide the simplified numerator by the simplified denominator: \[ \frac{18}{\frac{9}{16}} = 18 \times \frac{16}{9} \]

Simplify the multiplication: \[ 18 \times \frac{16}{9} = \frac{18 \times 16}{9} = \frac{288}{9} \]

Simplify $\frac{288}{9}$: \[ \frac{288}{9} = 32 \]

\[ \boxed{32} \]

Was this solution helpful?

Unhelpful

Helpful