Write the Fraction in Simplest Form (2^-4)/(4^0)

$\frac{2^{- 4}}{4^{0}}$

Step 1

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

$\frac{1}{4^{0} \cdot 2^{4}}$

Step 2

Simplify the denominator.

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

$\frac{1}{{(2^{2})}^{0} \cdot 2^{4}}$

Multiply the exponents in ${(2^{2})}^{0}$ .

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

$\frac{1}{2^{2 \cdot 0} \cdot 2^{4}}$

Multiply $2$ by $0$ .

$\frac{1}{2^{0} \cdot 2^{4}}$

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

$\frac{1}{2^{0 + 4}}$

Add $0$ and $4$ .

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

Step 3

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

$\frac{1}{16}$