Evaluate 4/7(2/3)^2-1/9

$\frac{4}{7} {(\frac{2}{3})}^{2} - \frac{1}{9}$

Step 1

Simplify each term.

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

$\frac{4}{7} \cdot \frac{2^{2}}{3^{2}} - \frac{1}{9}$

Combine.

$\frac{4 \cdot 2^{2}}{7 \cdot 3^{2}} - \frac{1}{9}$

Simplify the numerator.

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

$\frac{2^{2} \cdot 2^{2}}{7 \cdot 3^{2}} - \frac{1}{9}$

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

$\frac{2^{2 + 2}}{7 \cdot 3^{2}} - \frac{1}{9}$

Add $2$ and $2$ .

$\frac{2^{4}}{7 \cdot 3^{2}} - \frac{1}{9}$

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

$\frac{2^{4}}{7 \cdot 9} - \frac{1}{9}$

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

$\frac{16}{7 \cdot 9} - \frac{1}{9}$

Multiply $7$ by $9$ .

$\frac{16}{63} - \frac{1}{9}$

Step 2

To write $- \frac{1}{9}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{16}{63} - \frac{1}{9} \cdot \frac{7}{7}$

Step 3

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

Multiply $\frac{1}{9}$ by $\frac{7}{7}$ .

$\frac{16}{63} - \frac{7}{9 \cdot 7}$

Multiply $9$ by $7$ .

$\frac{16}{63} - \frac{7}{63}$

Step 4

Simplify the expression.

Combine the numerators over the common denominator.

$\frac{16 - 7}{63}$

Subtract $7$ from $16$ .

$\frac{9}{63}$

Step 5

Cancel the common factor of $9$ and $63$ .

Factor $9$ out of $9$ .

$\frac{9 (1)}{63}$

Cancel the common factors.

Factor $9$ out of $63$ .

$\frac{9 \cdot 1}{9 \cdot 7}$

Cancel the common factor.

$\frac{9 \cdot 1}{9 \cdot 7}$

Rewrite the expression.

$\frac{1}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7}$

Decimal Form:

$0.\overline{142857}$

Evaluate 4/7(2/3)^2-1/9

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