Simplify ((4^2)^-1)/(4^-1)

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

Step 1

Move ${(4^{2})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{4^{- 1} \cdot 4^{2}}$

Step 2

Simplify the denominator.

Multiply $4^{- 1}$ by $4^{2}$ by adding the exponents.

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

$\frac{1}{4^{- 1 + 2}}$

Add $- 1$ and $2$ .

$\frac{1}{4^{1}}$

Simplify $4^{1}$ .

$\frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$