Question

evaluate \\(\frac{2^{-4}}{4^0}\\). write your answer as a fraction in simplest form. the solution is \\(square\\).

Explanation:

Step1: Simplify the numerator using negative exponent rule

Recall that \(a^{-n}=\frac{1}{a^{n}}\), so \(2^{-4}=\frac{1}{2^{4}}\). Calculate \(2^{4}=16\), so \(2^{-4}=\frac{1}{16}\).

Step2: Simplify the denominator using zero exponent rule

Recall that \(a^{0} = 1\) for \(a
eq0\), so \(4^{0}=1\).

Step3: Divide the numerator by the denominator

Now we have \(\frac{\frac{1}{16}}{1}\), and dividing a number by 1 gives the number itself, so \(\frac{\frac{1}{16}}{1}=\frac{1}{16}\).

Answer:

\(\frac{1}{16}\)