Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{3}}{2^{3}} + \frac{2}{3}$

Step 1.2

One to any power is one.

$\frac{1}{2^{3}} + \frac{2}{3}$

Step 1.3

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

$\frac{1}{8} + \frac{2}{3}$

Step 2

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{8} \cdot \frac{3}{3} + \frac{2}{3}$

Step 3

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{8} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{8}{8}$

Step 4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{8}$ by $\frac{3}{3}$ .

$\frac{3}{8 \cdot 3} + \frac{2}{3} \cdot \frac{8}{8}$

Step 4.2

Multiply $8$ by $3$ .

$\frac{3}{24} + \frac{2}{3} \cdot \frac{8}{8}$

Step 4.3

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{3}{24} + \frac{2 \cdot 8}{3 \cdot 8}$

Step 4.4

Multiply $3$ by $8$ .

$\frac{3}{24} + \frac{2 \cdot 8}{24}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 + 2 \cdot 8}{24}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $8$ .

$\frac{3 + 16}{24}$

Step 6.2

Add $3$ and $16$ .

$\frac{19}{24}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{24}$

Decimal Form:

$0.791\overline{6}$