Evaluate (2/3-5/9)^2

${(\frac{2}{3} - \frac{5}{9})}^{2}$

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(\frac{2}{3} \cdot \frac{3}{3} - \frac{5}{9})}^{2}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{3}{3}$ .

${(\frac{2 \cdot 3}{3 \cdot 3} - \frac{5}{9})}^{2}$

Multiply $3$ by $3$ .

${(\frac{2 \cdot 3}{9} - \frac{5}{9})}^{2}$

Combine the numerators over the common denominator.

${(\frac{2 \cdot 3 - 5}{9})}^{2}$

Simplify the numerator.

Multiply $2$ by $3$ .

${(\frac{6 - 5}{9})}^{2}$

Subtract $5$ from $6$ .

${(\frac{1}{9})}^{2}$

Apply the product rule to $\frac{1}{9}$ .

$\frac{1^{2}}{9^{2}}$

One to any power is one.

$\frac{1}{9^{2}}$

Raise $9$ to the power of $2$ .

$\frac{1}{81}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{81}$

Decimal Form:

$0.01234567 \dots$