Solve Fraction with Negative Exponent: 2/4^(-2)

$\frac{2}{4^{-2}}=\text{?}$

First, let's note that 4 is a power of 2:

$4=2^2$therefore we can perform a conversion to a common base for all terms in the problem,

Let's apply this:

$\frac{2}{4^{-2}}=\frac{2}{(2^2)^{-2}}$Next, we'll use the power law for power of power:

$(a^m)^n=a^{m\cdot n}$and we'll apply this law to the denominator term we got in the last step:

$\frac{2}{(2^2)^{-2}}=\frac{2}{2^{2\cdot(-2)}}=\frac{2}{2^{-4}}$where in the first step we applied the above law to the denominator and in the second step we simplified the expression we got,

Next, we'll use the power law for division between terms with identical bases:

$\frac{a^m}{a^n}=a^{m-n}$and we'll apply this law to the last expression we got:

$\frac{2}{2^{-4}}=2^{1-(-4)}=2^{1+4}=2^5$

Therefore the correct answer is answer B.