Question

What is the simplified value of the exponential expression 16^1/4?

Answer 1

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:

$\sqrt[4]{2^4}=2$