Algebra Examples

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

Step 1

Anything raised to $0$ is $1$ .

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

Step 2

Multiply $5^{- 2}$ by $1$ .

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

Step 3

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

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

Step 4

Raise $5$ to the power of $2$ .

$\frac{1}{25} \cdot 6^{- 1} \cdot (100^{0} (\frac{1}{2^{- 1}}))$

Step 5

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

$\frac{1}{25} \cdot \frac{1}{6} \cdot (100^{0} (\frac{1}{2^{- 1}}))$

Step 6

Multiply $\frac{1}{25} \cdot \frac{1}{6}$ .

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Step 6.1

Multiply $\frac{1}{25}$ by $\frac{1}{6}$ .

$\frac{1}{25 \cdot 6} \cdot (100^{0} (\frac{1}{2^{- 1}}))$

Step 6.2

Multiply $25$ by $6$ .

$\frac{1}{150} \cdot (100^{0} (\frac{1}{2^{- 1}}))$

Step 7

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

$\frac{1}{150} \cdot (100^{0} \frac{1}{\frac{1}{2}})$

Step 8

Simplify the expression.

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Step 8.1

Anything raised to $0$ is $1$ .

$\frac{1}{150} \cdot (1 \frac{1}{\frac{1}{2}})$

Step 8.2

Multiply $\frac{1}{\frac{1}{2}}$ by $1$ .

$\frac{1}{150} \cdot \frac{1}{\frac{1}{2}}$

Step 8.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{150} \cdot (1 \cdot 2)$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Factor $2$ out of $150$ .

$\frac{1}{2 (75)} \cdot (1 \cdot 2)$

Step 9.2

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

$\frac{1}{2 (75)} \cdot (2 \cdot 1)$

Step 9.3

Cancel the common factor.

$\frac{1}{2 \cdot 75} \cdot (2 \cdot 1)$

Step 9.4

Rewrite the expression.

$\frac{1}{75}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{75}$

Decimal Form:

$0.01\overline{3}$