Write the following in simplified radical form. $$ \sqrt[5]{v^{9}} $$ Ascume that the variable renresents a mositive

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UpStudy AI · Accepted Answer

We start with:
$$
\sqrt[5]{v^9}
$$
Express the exponent as a sum that facilitates the extraction of a perfect 5th power:
$$
v^9 = v^5 \cdot v^4
$$
Now, taking the 5th root gives:
$$
\sqrt[5]{v^9} = \sqrt[5]{v^5 \cdot v^4} = \sqrt[5]{v^5} \cdot \sqrt[5]{v^4}
$$
Since $$ v $$ is positive, we have:
$$
\sqrt[5]{v^5} = v
$$
Thus, the simplified radical form is:
$$
v \sqrt[5]{v^4}
$$
The simplified radical form is $$ v \sqrt[5]{v^4} $$.

Write the following in simplified radical form.

Ascume that the variable renresents a mositive

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Write the following in simplified radical form. Ascume that the variable renresents a mositive