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

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

Step 1

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

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

Step 2

Simplify the denominator.

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

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

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

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

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

Multiply $2$ by $2$ .

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

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

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

Add $- 4$ and $4$ .

$\frac{1}{2^{0}}$

Step 3

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 4

Divide $1$ by $1$ .

$1$