Question

3 multiple choice 1 point evaluate: \\(\frac{2^{-4}}{4^0}\\) \\(\bigcirc\\) 2 \\(\bigcirc\\) \\(\frac{1}{16}\\) \\(\bigcirc\\) \\(-\frac{1}{16}\\) \\(\bigcirc\\) 8 clear my selection previous next

Explanation:

Step1: Simplify the numerator

Recall the negative exponent rule: \(a^{-n}=\frac{1}{a^{n}}\). So for \(2^{-4}\), we have \(2^{-4}=\frac{1}{2^{4}}\). Calculate \(2^{4}=16\), so \(2^{-4}=\frac{1}{16}\).

Step2: Simplify the denominator

Recall the zero - exponent rule: \(a^{0} = 1\) (where \(a
eq0\)). For \(4^{0}\), since \(4
eq0\), \(4^{0}=1\).

Step3: Divide the numerator by the denominator

Now we have \(\frac{2^{-4}}{4^{0}}=\frac{\frac{1}{16}}{1}\). Dividing a number by 1 gives the number itself, so \(\frac{\frac{1}{16}}{1}=\frac{1}{16}\).

Answer:

\(\frac{1}{16}\) (the option corresponding to \(\frac{1}{16}\))