Simplify (4^0)(5^-5)(100)^0(1/(2^-1))

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

Step 1

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

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

Step 2

Anything raised to $0$ is $1$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Simplify the expression.

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

$\frac{1}{3125} {(100)}^{0} \frac{1}{\frac{1}{2}}$

Anything raised to $0$ is $1$ .

$\frac{1}{3125} \cdot 1 \frac{1}{\frac{1}{2}}$

Multiply $\frac{1}{3125}$ by $1$ .

$\frac{1}{3125} \cdot \frac{1}{\frac{1}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{3125} (1 \cdot 2)$

Multiply $2$ by $1$ .

$\frac{1}{3125} \cdot 2$

Step 6

Combine $\frac{1}{3125}$ and $2$ .

$\frac{2}{3125}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3125}$

Decimal Form:

$0.00064$