Algebra Examples

$(4^{0}) (5^{- 1}) (6^{- 1}) (100^{0}) (\frac{1}{2^{- 1}})$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(4^{0}) (5^{- 1}) (6^{- 1}) (100^{0}) \frac{1}{\frac{1}{2}}$

Step 2

Anything raised to $0$ is $1$ .

$1 \cdot 5^{- 1} \cdot 6^{- 1} \cdot 100^{0} \frac{1}{\frac{1}{2}}$

Step 3

Multiply $5^{- 1}$ by $1$ .

$5^{- 1} \cdot 6^{- 1} \cdot 100^{0} \frac{1}{\frac{1}{2}}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{5} \cdot 6^{- 1} \cdot 100^{0} \frac{1}{\frac{1}{2}}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{5} \cdot \frac{1}{6} \cdot 100^{0} \frac{1}{\frac{1}{2}}$

Step 6

Multiply $\frac{1}{5} \cdot \frac{1}{6}$ .

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Step 6.1

Multiply $\frac{1}{5}$ by $\frac{1}{6}$ .

$\frac{1}{5 \cdot 6} \cdot 100^{0} \frac{1}{\frac{1}{2}}$

Step 6.2

Multiply $5$ by $6$ .

$\frac{1}{30} \cdot 100^{0} \frac{1}{\frac{1}{2}}$

Step 7

Simplify the expression.

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Step 7.1

Anything raised to $0$ is $1$ .

$\frac{1}{30} \cdot 1 \frac{1}{\frac{1}{2}}$

Step 7.2

Multiply $\frac{1}{30}$ by $1$ .

$\frac{1}{30} \cdot \frac{1}{\frac{1}{2}}$

Step 7.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{30} (1 \cdot 2)$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Factor $2$ out of $30$ .

$\frac{1}{2 (15)} (1 \cdot 2)$

Step 8.2

Factor $2$ out of $1 \cdot 2$ .

$\frac{1}{2 (15)} (2 \cdot 1)$

Step 8.3

Cancel the common factor.

$\frac{1}{2 \cdot 15} (2 \cdot 1)$

Step 8.4

Rewrite the expression.

$\frac{1}{15}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{15}$

Decimal Form:

$0.0\overline{6}$