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

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

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

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

Subtract $2$ from $- 1$ .

$\frac{1}{4^{- 3}}$

Step 3

Move $4^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4^{3}$

Step 4

Raise $4$ to the power of $3$ .

$64$