Simplify 2/(4^-4)

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

Step 1

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

$2 \cdot 4^{4}$

Step 2

Rewrite $4$ as $2^{2}$ .

$2 \cdot {(2^{2})}^{4}$

Step 3

Multiply the exponents in ${(2^{2})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 \cdot 2^{2 \cdot 4}$

Multiply $2$ by $4$ .

$2 \cdot 2^{8}$

Step 4

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

$2^{1 + 8}$

Step 5

Add $1$ and $8$ .

$2^{9}$

Step 6

Raise $2$ to the power of $9$ .

$512$