Basic Math Examples

7^{- 1} + 2^{- 1}

$7^{- 1} + 2^{- 1}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{7} + 2^{- 1}$

Step 1.2

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{7} + \frac{1}{2}$

Step 2

To write

$\frac{1}{7}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{1}{7} \cdot \frac{2}{2} + \frac{1}{2}$

Step 3

To write

$\frac{1}{2}$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$\frac{1}{7} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of

$14$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{1}{7}$ by

$\frac{2}{2}$ .

$\frac{2}{7 \cdot 2} + \frac{1}{2} \cdot \frac{7}{7}$

Step 4.2

Multiply

$7$ by

$2$ .

$\frac{2}{14} + \frac{1}{2} \cdot \frac{7}{7}$

Step 4.3

Multiply

$\frac{1}{2}$ by

$\frac{7}{7}$ .

$\frac{2}{14} + \frac{7}{2 \cdot 7}$

Step 4.4

Multiply

$2$ by

$7$ .

$\frac{2}{14} + \frac{7}{14}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 + 7}{14}$

Step 6

Add

$2$ and

$7$ .

$\frac{9}{14}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{14}$

Decimal Form:

$0.6\overline{428571}$