Question

Rewrite −−−^3√8x^9 using rational exponents. (1 point)

Answer 1

To rewrite \(-\sqrt[3]{8x^9}\) using rational exponents, we can express the cube root and the powers as follows:

\[
-\sqrt[3]{8x^9} = - (8x^9)^{\frac{1}{3}}
\]

Now, we can separate the components inside the parentheses:

\[
= - (8^{\frac{1}{3}})(x^{9 \cdot \frac{1}{3}})
\]

Calculating \(8^{\frac{1}{3}}\):

\[
8^{\frac{1}{3}} = 2
\]

And for \(x^{9 \cdot \frac{1}{3}} = x^3\):

Putting it all together, we have:

\[
= - (2)(x^3) = -2x^3
\]

Thus, \(-\sqrt[3]{8x^9}\) rewritten using rational exponents is:

\[
-2x^3
\]