Simplify (4^05^-26^-1*100^0)/(2^-1)

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

Step 1

Simplify the expression.

Move $5^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Move $6^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Move $2^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2}{5^{2} \cdot 6}$

Step 2

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $5^{2} \cdot 6$ .

$\frac{2 (1)}{2 (5^{2} \cdot 3)}$

Cancel the common factor.

$\frac{2 \cdot 1}{2 (5^{2} \cdot 3)}$

Rewrite the expression.

$\frac{1}{5^{2} \cdot 3}$

Step 3

Simplify the expression.

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

$\frac{1}{25 \cdot 3}$

Multiply $25$ by $3$ .

$\frac{1}{75}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{75}$

Decimal Form:

$0.01\overline{3}$

Simplify (4^0*5^-2*6^-1*100^0)/(2^-1)