Evaluate ((4/5)^2)÷(4/5-1/15)

${(\frac{4}{5})}^{2} \div (\frac{4}{5} - \frac{1}{15})$

Step 1

Rewrite the division as a fraction.

$\frac{{(\frac{4}{5})}^{2}}{\frac{4}{5} - \frac{1}{15}}$

Step 2

Simplify the numerator.

Apply the product rule to $\frac{4}{5}$ .

$\frac{\frac{4^{2}}{5^{2}}}{\frac{4}{5} - \frac{1}{15}}$

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

$\frac{\frac{16}{5^{2}}}{\frac{4}{5} - \frac{1}{15}}$

Raise $5$ to the power of $2$ .

$\frac{\frac{16}{25}}{\frac{4}{5} - \frac{1}{15}}$

Step 3

Simplify the denominator.

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{16}{25}}{\frac{4}{5} \cdot \frac{3}{3} - \frac{1}{15}}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4}{5}$ by $\frac{3}{3}$ .

$\frac{\frac{16}{25}}{\frac{4 \cdot 3}{5 \cdot 3} - \frac{1}{15}}$

Multiply $5$ by $3$ .

$\frac{\frac{16}{25}}{\frac{4 \cdot 3}{15} - \frac{1}{15}}$

Combine the numerators over the common denominator.

$\frac{\frac{16}{25}}{\frac{4 \cdot 3 - 1}{15}}$

Simplify the numerator.

Multiply $4$ by $3$ .

$\frac{\frac{16}{25}}{\frac{12 - 1}{15}}$

Subtract $1$ from $12$ .

$\frac{\frac{16}{25}}{\frac{11}{15}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{16}{25} \cdot \frac{15}{11}$

Step 5

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

$\frac{16}{5 (5)} \cdot \frac{15}{11}$

Factor $5$ out of $15$ .

$\frac{16}{5 \cdot 5} \cdot \frac{5 \cdot 3}{11}$

Cancel the common factor.

$\frac{16}{5 \cdot 5} \cdot \frac{5 \cdot 3}{11}$

Rewrite the expression.

$\frac{16}{5} \cdot \frac{3}{11}$

Step 6

Multiply $\frac{16}{5}$ by $\frac{3}{11}$ .

$\frac{16 \cdot 3}{5 \cdot 11}$

Step 7

Multiply.

Multiply $16$ by $3$ .

$\frac{48}{5 \cdot 11}$

Multiply $5$ by $11$ .

$\frac{48}{55}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{48}{55}$

Decimal Form:

$0.8\overline{72}$

Evaluate ((4/5)^2)÷(4/5-1/15)

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