Algebra Examples

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

Step 1

Anything raised to $0$ is $1$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Simplify the expression.

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Step 6.1

Anything raised to $0$ is $1$ .

$\frac{1}{25} \cdot (1 \frac{1}{\frac{1}{2}})$

Step 6.2

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

$\frac{1}{25} \cdot \frac{1}{\frac{1}{2}}$

Step 6.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{25} \cdot (1 \cdot 2)$

Step 6.4

Multiply $2$ by $1$ .

$\frac{1}{25} \cdot 2$

Step 7

Combine $\frac{1}{25}$ and $2$ .

$\frac{2}{25}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{25}$

Decimal Form:

$0.08$