Basic Math Examples

${(\frac{2}{3})}^{3} - 13 {(\frac{2}{3})}^{2} + 16 (\frac{2}{3}) + 4$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{2^{3}}{3^{3}} - 13 {(\frac{2}{3})}^{2} + 16 (\frac{2}{3}) + 4$

Step 1.2

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

$\frac{8}{3^{3}} - 13 {(\frac{2}{3})}^{2} + 16 (\frac{2}{3}) + 4$

Step 1.3

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

$\frac{8}{27} - 13 {(\frac{2}{3})}^{2} + 16 (\frac{2}{3}) + 4$

Step 1.4

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

$\frac{8}{27} - 13 \frac{2^{2}}{3^{2}} + 16 (\frac{2}{3}) + 4$

Step 1.5

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

$\frac{8}{27} - 13 \frac{4}{3^{2}} + 16 (\frac{2}{3}) + 4$

Step 1.6

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

$\frac{8}{27} - 13 (\frac{4}{9}) + 16 (\frac{2}{3}) + 4$

Step 1.7

Multiply $- 13 (\frac{4}{9})$ .

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Step 1.7.1

Combine $- 13$ and $\frac{4}{9}$ .

$\frac{8}{27} + \frac{- 13 \cdot 4}{9} + 16 (\frac{2}{3}) + 4$

Step 1.7.2

Multiply $- 13$ by $4$ .

$\frac{8}{27} + \frac{- 52}{9} + 16 (\frac{2}{3}) + 4$

Step 1.8

Move the negative in front of the fraction.

$\frac{8}{27} - \frac{52}{9} + 16 (\frac{2}{3}) + 4$

Step 1.9

Multiply $16 (\frac{2}{3})$ .

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Step 1.9.1

Combine $16$ and $\frac{2}{3}$ .

$\frac{8}{27} - \frac{52}{9} + \frac{16 \cdot 2}{3} + 4$

Step 1.9.2

Multiply $16$ by $2$ .

$\frac{8}{27} - \frac{52}{9} + \frac{32}{3} + 4$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{52}{9}$ by $\frac{3}{3}$ .

$\frac{8}{27} - (\frac{52}{9} \cdot \frac{3}{3}) + \frac{32}{3} + 4$

Step 2.2

Multiply $\frac{52}{9}$ by $\frac{3}{3}$ .

$\frac{8}{27} - \frac{52 \cdot 3}{9 \cdot 3} + \frac{32}{3} + 4$

Step 2.3

Multiply $\frac{32}{3}$ by $\frac{9}{9}$ .

$\frac{8}{27} - \frac{52 \cdot 3}{9 \cdot 3} + \frac{32}{3} \cdot \frac{9}{9} + 4$

Step 2.4

Multiply $\frac{32}{3}$ by $\frac{9}{9}$ .

$\frac{8}{27} - \frac{52 \cdot 3}{9 \cdot 3} + \frac{32 \cdot 9}{3 \cdot 9} + 4$

Step 2.5

Write $4$ as a fraction with denominator $1$ .

$\frac{8}{27} - \frac{52 \cdot 3}{9 \cdot 3} + \frac{32 \cdot 9}{3 \cdot 9} + \frac{4}{1}$

Step 2.6

Multiply $\frac{4}{1}$ by $\frac{27}{27}$ .

$\frac{8}{27} - \frac{52 \cdot 3}{9 \cdot 3} + \frac{32 \cdot 9}{3 \cdot 9} + \frac{4}{1} \cdot \frac{27}{27}$

Step 2.7

Multiply $\frac{4}{1}$ by $\frac{27}{27}$ .

$\frac{8}{27} - \frac{52 \cdot 3}{9 \cdot 3} + \frac{32 \cdot 9}{3 \cdot 9} + \frac{4 \cdot 27}{27}$

Step 2.8

Reorder the factors of $9 \cdot 3$ .

$\frac{8}{27} - \frac{52 \cdot 3}{3 \cdot 9} + \frac{32 \cdot 9}{3 \cdot 9} + \frac{4 \cdot 27}{27}$

Step 2.9

Multiply $3$ by $9$ .

$\frac{8}{27} - \frac{52 \cdot 3}{27} + \frac{32 \cdot 9}{3 \cdot 9} + \frac{4 \cdot 27}{27}$

Step 2.10

Multiply $3$ by $9$ .

$\frac{8}{27} - \frac{52 \cdot 3}{27} + \frac{32 \cdot 9}{27} + \frac{4 \cdot 27}{27}$

Step 3

Combine the numerators over the common denominator.

$\frac{8 - 52 \cdot 3 + 32 \cdot 9 + 4 \cdot 27}{27}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 52$ by $3$ .

$\frac{8 - 156 + 32 \cdot 9 + 4 \cdot 27}{27}$

Step 4.2

Multiply $32$ by $9$ .

$\frac{8 - 156 + 288 + 4 \cdot 27}{27}$

Step 4.3

Multiply $4$ by $27$ .

$\frac{8 - 156 + 288 + 108}{27}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $156$ from $8$ .

$\frac{- 148 + 288 + 108}{27}$

Step 5.2

Add $- 148$ and $288$ .

$\frac{140 + 108}{27}$

Step 5.3

Add $140$ and $108$ .

$\frac{248}{27}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{248}{27}$

Decimal Form:

$9.\overline{185}$

Mixed Number Form:

$9 \frac{5}{27}$