Basic Math Examples

$\frac{9}{10} \cdot {(\frac{2}{3})}^{3} + \frac{2}{3}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{9}{10} \cdot \frac{2^{3}}{3^{3}} + \frac{2}{3}$

Step 1.2

Combine.

$\frac{9 \cdot 2^{3}}{10 \cdot 3^{3}} + \frac{2}{3}$

Step 1.3

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

$\frac{9 \cdot 8}{10 \cdot 3^{3}} + \frac{2}{3}$

Step 1.4

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

$\frac{9 \cdot 8}{10 \cdot 27} + \frac{2}{3}$

Step 1.5

Multiply $9$ by $8$ .

$\frac{72}{10 \cdot 27} + \frac{2}{3}$

Step 1.6

Multiply $10$ by $27$ .

$\frac{72}{270} + \frac{2}{3}$

Step 1.7

Cancel the common factor of $72$ and $270$ .

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Step 1.7.1

Factor $18$ out of $72$ .

$\frac{18 (4)}{270} + \frac{2}{3}$

Step 1.7.2

Cancel the common factors.

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Step 1.7.2.1

Factor $18$ out of $270$ .

$\frac{18 \cdot 4}{18 \cdot 15} + \frac{2}{3}$

Step 1.7.2.2

Cancel the common factor.

$\frac{18 \cdot 4}{18 \cdot 15} + \frac{2}{3}$

Step 1.7.2.3

Rewrite the expression.

$\frac{4}{15} + \frac{2}{3}$

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4}{15} + \frac{2}{3} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$\frac{4}{15} + \frac{2 \cdot 5}{3 \cdot 5}$

Step 3.2

Multiply $3$ by $5$ .

$\frac{4}{15} + \frac{2 \cdot 5}{15}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 + 2 \cdot 5}{15}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $5$ .

$\frac{4 + 10}{15}$

Step 5.2

Add $4$ and $10$ .

$\frac{14}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{14}{15}$

Decimal Form:

$0.9\overline{3}$