Simplify ((-4)^-2)÷(4^-4)

${(- 4)}^{- 2} \div 4^{- 4}$

Step 1

Rewrite the division as a fraction.

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

Step 2

Simplify the expression.

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

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

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

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

Step 3

Cancel the common factor of $4^{4}$ and ${(- 4)}^{2}$ .

Rewrite $4$ as $- 1 (- 4)$ .

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

Apply the product rule to $- 1 (- 4)$ .

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

Raise $- 1$ to the power of $4$ .

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

Multiply ${(- 4)}^{4}$ by $1$ .

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

Factor ${(- 4)}^{2}$ out of ${(- 4)}^{4}$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide ${(- 4)}^{2}$ by $1$ .

${(- 4)}^{2}$

Step 4

Raise $- 4$ to the power of $2$ .

$16$