Answer
2
Explanation
First, we are going to use the law of fractional exponents: \(a^{\frac{1}{n} =\sqrt[n]{a}\)
We can infer form our expression that \(a=16\) and \(n=4\), so let's replace the values:
\(a^{\frac{1}{n} =\sqrt[n]{a}\)
\(16^{\frac{1}{4} }=\sqrt[4]{16}\)
Notice that we can also decompose 16 into prime factors to get \(16=2^4\), so we can rewrite our expression as follows:
\(\sqrt[4]{16}=\sqrt[4]{2^4}\)
Finally, we can use the rule of radicals: \(\sqrt[n]{a^n} =a\), so:
\(\sqrt[4]{2^4}=2\)
