Question

Find the cube root of 8. Then, rewrite rational exponents as radicals and simplify.

Answer 1

To find the cube root of 8, we can express this as:

\[
\sqrt[3]{8}
\]

The cube root of 8 is 2, since \(2 \times 2 \times 2 = 8\). So, we have:

\[
\sqrt[3]{8} = 2
\]

Next, we can rewrite rational exponents as radicals. The expression for the cube root can be written as:

\[
8^{\frac{1}{3}}
\]

Now, to rewrite this using radicals, we have:

\[
8^{\frac{1}{3}} = \sqrt[3]{8}
\]

Since we already know that \(\sqrt[3]{8} = 2\), we have the simplified result:

\[
2
\]

Therefore, the cube root of 8, expressed with rational exponents as radicals and simplified, is:

\[
\sqrt[3]{8} = 2
\]