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:

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

Answer 2

The simplified value of the exponential expression $16^\frac{1}{4}$ is $2$.

What does Fractional power mean for an integer?

Fractional power implies the root of the strength of the denominator of that integer.

For example: $a^\frac{1}{n}=\sqrt[n]{a}$.

Given here the exponential expression is $16^\frac{1}{4}$

So here $a=16,n=4$

We know that, $2^4=16$

Thus, $16^\frac{1}{4}=\sqrt[4]{16}=\sqrt[4]{2^4}=2$

Hence the equivalent value of the given expression $16^\frac{1}{4}$ is 2.

Learn more about Fractional Power here -

https://brainly.com/question/13689764

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