Evaluate (2^-25^0)/(2^35^-2)

$\frac{2^{- 2} \cdot 5^{0}}{2^{3} \cdot 5^{- 2}}$

Step 1

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

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

Step 2

Multiply $2^{3}$ by $2^{2}$ by adding the exponents.

Move $2^{2}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $3$ .

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

Step 3

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

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

Step 4

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

$\frac{25}{2^{5}}$

Step 5

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

$\frac{25}{32}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{32}$

Decimal Form:

$0.78125$

Evaluate (2^-2*5^0)/(2^3*5^-2)