Evaluate 4/7(2/3)^2+8/9

$\frac{4}{7} {(\frac{2}{3})}^{2} + \frac{8}{9}$

Simplify each term.

Apply the product rule to $\frac{2}{3}$ .

$\frac{4}{7} \cdot \frac{2^{2}}{3^{2}} + \frac{8}{9}$

Combine.

$\frac{4 \cdot 2^{2}}{7 \cdot 3^{2}} + \frac{8}{9}$

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$\frac{2^{2} \cdot 2^{2}}{7 \cdot 3^{2}} + \frac{8}{9}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2^{2 + 2}}{7 \cdot 3^{2}} + \frac{8}{9}$

Add $2$ and $2$ .

$\frac{2^{4}}{7 \cdot 3^{2}} + \frac{8}{9}$

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

$\frac{2^{4}}{7 \cdot 9} + \frac{8}{9}$

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

$\frac{16}{7 \cdot 9} + \frac{8}{9}$

Multiply $7$ by $9$ .

$\frac{16}{63} + \frac{8}{9}$

To write $\frac{8}{9}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{16}{63} + \frac{8}{9} \cdot \frac{7}{7}$

Write each expression with a common denominator of $63$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{9}$ by $\frac{7}{7}$ .

$\frac{16}{63} + \frac{8 \cdot 7}{9 \cdot 7}$

Multiply $9$ by $7$ .

$\frac{16}{63} + \frac{8 \cdot 7}{63}$

Combine the numerators over the common denominator.

$\frac{16 + 8 \cdot 7}{63}$

Simplify the numerator.

Multiply $8$ by $7$ .

$\frac{16 + 56}{63}$

Add $16$ and $56$ .

$\frac{72}{63}$

Cancel the common factor of $72$ and $63$ .

Factor $9$ out of $72$ .

$\frac{9 (8)}{63}$

Cancel the common factors.

Factor $9$ out of $63$ .

$\frac{9 \cdot 8}{9 \cdot 7}$

Cancel the common factor.

$\frac{9 \cdot 8}{9 \cdot 7}$

Rewrite the expression.

$\frac{8}{7}$

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{7}$

Decimal Form:

$1.\overline{142857}$

Mixed Number Form:

$1 \frac{1}{7}$

Evaluate 4/7(2/3)^2+8/9

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