Basic Math Examples

4^{- 1} + 6^{- 1}

$4^{- 1} + 6^{- 1}$

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}}

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

\frac{1}{4} + 6^{- 1}

$\frac{1}{4} + 6^{- 1}$

Step 1.2

Rewrite the expression using the negative exponent rule

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

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

\frac{1}{4} + \frac{1}{6}

$\frac{1}{4} + \frac{1}{6}$

\frac{1}{4} + \frac{1}{6}

$\frac{1}{4} + \frac{1}{6}$

Step 2

To write

\frac{1}{4}

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6}

$\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6}$

Step 3

To write

\frac{1}{6}

$\frac{1}{6}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{2}{2}

$\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of

12

$12$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{1}{4}

$\frac{1}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2}

$\frac{3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2}$

Step 4.2

Multiply

4

$4$ by

3

$3$ .

\frac{3}{12} + \frac{1}{6} \cdot \frac{2}{2}

$\frac{3}{12} + \frac{1}{6} \cdot \frac{2}{2}$

Step 4.3

Multiply

$\frac{1}{6}$ by

$\frac{2}{2}$ .

$\frac{3}{12} + \frac{2}{6 \cdot 2}$

Step 4.4

Multiply

$6$ by

$2$ .

$\frac{3}{12} + \frac{2}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 + 2}{12}$

Step 6

Add

$3$ and

$2$ .

$\frac{5}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{12}$

Decimal Form:

$0.41\overline{6}$