Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

$\frac{8}{3^{3}} + \frac{1}{9} + \frac{1}{3} \cdot \frac{7}{3}$

Step 1.3

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

$\frac{8}{27} + \frac{1}{9} + \frac{1}{3} \cdot \frac{7}{3}$

Step 1.4

Multiply $\frac{1}{3} \cdot \frac{7}{3}$ .

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Step 1.4.1

Multiply $\frac{1}{3}$ by $\frac{7}{3}$ .

$\frac{8}{27} + \frac{1}{9} + \frac{7}{3 \cdot 3}$

Step 1.4.2

Multiply $3$ by $3$ .

$\frac{8}{27} + \frac{1}{9} + \frac{7}{9}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{8}{27} + \frac{1 + 7}{9}$

Step 2.2

Add $1$ and $7$ .

$\frac{8}{27} + \frac{8}{9}$

Step 3

To write $\frac{8}{9}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8}{27} + \frac{8}{9} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $27$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{8}{9}$ by $\frac{3}{3}$ .

$\frac{8}{27} + \frac{8 \cdot 3}{9 \cdot 3}$

Step 4.2

Multiply $9$ by $3$ .

$\frac{8}{27} + \frac{8 \cdot 3}{27}$

Step 5

Combine the numerators over the common denominator.

$\frac{8 + 8 \cdot 3}{27}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $8$ by $3$ .

$\frac{8 + 24}{27}$

Step 6.2

Add $8$ and $24$ .

$\frac{32}{27}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{32}{27}$

Decimal Form:

$1.\overline{185}$

Mixed Number Form:

$1 \frac{5}{27}$