Evaluate (((-2)^2+1/3)^2)/(26/9)

$\frac{{({(- 2)}^{2} + \frac{1}{3})}^{2}}{\frac{26}{9}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

${({(- 2)}^{2} + \frac{1}{3})}^{2} \frac{9}{26}$

Step 2

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

${(4 + \frac{1}{3})}^{2} \frac{9}{26}$

Step 3

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

${(4 \cdot \frac{3}{3} + \frac{1}{3})}^{2} \frac{9}{26}$

Step 4

Combine $4$ and $\frac{3}{3}$ .

${(\frac{4 \cdot 3}{3} + \frac{1}{3})}^{2} \frac{9}{26}$

Step 5

Combine the numerators over the common denominator.

${(\frac{4 \cdot 3 + 1}{3})}^{2} \frac{9}{26}$

Step 6

Simplify the numerator.

Multiply $4$ by $3$ .

${(\frac{12 + 1}{3})}^{2} \frac{9}{26}$

Add $12$ and $1$ .

${(\frac{13}{3})}^{2} \frac{9}{26}$

Step 7

Apply the product rule to $\frac{13}{3}$ .

$\frac{13^{2}}{3^{2}} \cdot \frac{9}{26}$

Step 8

Combine.

$\frac{13^{2} \cdot 9}{3^{2} \cdot 26}$

Step 9

Simplify the expression.

Raise $13$ to the power of $2$ .

$\frac{169 \cdot 9}{3^{2} \cdot 26}$

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

$\frac{169 \cdot 9}{9 \cdot 26}$

Multiply $169$ by $9$ .

$\frac{1521}{9 \cdot 26}$

Multiply $9$ by $26$ .

$\frac{1521}{234}$

Step 10

Cancel the common factor of $1521$ and $234$ .

Factor $117$ out of $1521$ .

$\frac{117 (13)}{234}$

Cancel the common factors.

Factor $117$ out of $234$ .

$\frac{117 \cdot 13}{117 \cdot 2}$

Cancel the common factor.

$\frac{117 \cdot 13}{117 \cdot 2}$

Rewrite the expression.

$\frac{13}{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{2}$

Decimal Form:

$6.5$

Mixed Number Form:

$6 \frac{1}{2}$

Evaluate (((-2)^2+1/3)^2)/(26/9)

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