Basic Math Examples

${(\frac{1}{2})}^{3} + \frac{3}{4} \cdot \frac{1}{8}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1^{3}}{2^{3}} + \frac{3}{4} \cdot \frac{1}{8}$

Step 1.2

One to any power is one.

$\frac{1}{2^{3}} + \frac{3}{4} \cdot \frac{1}{8}$

Step 1.3

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

$\frac{1}{8} + \frac{3}{4} \cdot \frac{1}{8}$

Step 1.4

Multiply $\frac{3}{4} \cdot \frac{1}{8}$ .

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Step 1.4.1

Multiply $\frac{3}{4}$ by $\frac{1}{8}$ .

$\frac{1}{8} + \frac{3}{4 \cdot 8}$

Step 1.4.2

Multiply $4$ by $8$ .

$\frac{1}{8} + \frac{3}{32}$

Step 2

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{8} \cdot \frac{4}{4} + \frac{3}{32}$

Step 3

Write each expression with a common denominator of $32$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{8}$ by $\frac{4}{4}$ .

$\frac{4}{8 \cdot 4} + \frac{3}{32}$

Step 3.2

Multiply $8$ by $4$ .

$\frac{4}{32} + \frac{3}{32}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 + 3}{32}$

Step 5

Add $4$ and $3$ .

$\frac{7}{32}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{32}$

Decimal Form:

$0.21875$