Question

Use rational exponents to simplify the expression. If rational exponents appear after​ simplifying, write the answer in radical notation. Assume that all variables represent positive numbers.
RootIndex 16 StartRoot x Superscript 4 EndRoot
Question content area bottom
Part 1
RootIndex 16 StartRoot x Superscript 4 EndRootequals
  
enter your response here

Answer 1

To simplify the expression \(\sqrt[16]{x^4}\) using rational exponents, we can express it in the form of fractional exponents.

The 16th root of \(x^4\) can be rewritten using the property of exponents:

\[
\sqrt[16]{x^4} = x^{4/16}
\]

Now we simplify the exponent \(4/16\):

\[
4/16 = 1/4
\]

So, the expression becomes:

\[
x^{1/4}
\]

Now, we need to write this back in radical notation. The exponent \(1/4\) corresponds to the fourth root, so:

\[
x^{1/4} = \sqrt[4]{x}
\]

Therefore, the final simplified expression is:

\[
\sqrt[16]{x^4} = \sqrt[4]{x}
\]