Evaluate 5/8(1/3)^2+5/9

$\frac{5}{8} {(\frac{1}{3})}^{2} + \frac{5}{9}$

Simplify each term.

Apply the product rule to $\frac{1}{3}$ .

$\frac{5}{8} \cdot \frac{1^{2}}{3^{2}} + \frac{5}{9}$

Combine.

$\frac{5 \cdot 1^{2}}{8 \cdot 3^{2}} + \frac{5}{9}$

One to any power is one.

$\frac{5 \cdot 1}{8 \cdot 3^{2}} + \frac{5}{9}$

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

$\frac{5 \cdot 1}{8 \cdot 9} + \frac{5}{9}$

Multiply $5$ by $1$ .

$\frac{5}{8 \cdot 9} + \frac{5}{9}$

Multiply $8$ by $9$ .

$\frac{5}{72} + \frac{5}{9}$

To write $\frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{5}{72} + \frac{5}{9} \cdot \frac{8}{8}$

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{9}$ by $\frac{8}{8}$ .

$\frac{5}{72} + \frac{5 \cdot 8}{9 \cdot 8}$

Multiply $9$ by $8$ .

$\frac{5}{72} + \frac{5 \cdot 8}{72}$

Combine the numerators over the common denominator.

$\frac{5 + 5 \cdot 8}{72}$

Simplify the numerator.

Multiply $5$ by $8$ .

$\frac{5 + 40}{72}$

Add $5$ and $40$ .

$\frac{45}{72}$

Cancel the common factor of $45$ and $72$ .

Factor $9$ out of $45$ .

$\frac{9 (5)}{72}$

Cancel the common factors.

Factor $9$ out of $72$ .

$\frac{9 \cdot 5}{9 \cdot 8}$

Cancel the common factor.

$\frac{9 \cdot 5}{9 \cdot 8}$

Rewrite the expression.

$\frac{5}{8}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{8}$

Decimal Form:

$0.625$