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Write the following as a radical expression.

v^((6)/(7))

Write the following as a radical expression. $\newline$ $v^{\frac{6}{7}}$

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Evaluate integers raised to rational exponents

Full solution

Q. Write the following as a radical expression.

\newline

v^{\frac{6}{7}}

Given Expression Analysis: We are given the expression $v^{\frac{6}{7}}$ and asked to write it as a radical expression. $\newline$ To convert an exponent to a radical, we use the fact that $a^{\frac{m}{n}}$ is equivalent to the $n$ th root of $a$ raised to the $m$ power. $\newline$ In this case, we have $v$ raised to the power of $\frac{6}{7}$ , which means we are looking for the $7$ th root of $v$ raised to the $6$ th power.
Convert Exponent to Radical: Write the expression as a radical. $\newline$ The exponent $\frac{6}{7}$ indicates that we take the $7$ th root of $v$ and then raise it to the $6$ th power. $\newline$ So, $v^{\frac{6}{7}}$ is equivalent to the $7$ th root of $v^6$ .
Write as Radical: Check for any possible simplifications. $\newline$ Since there are no further simplifications that can be made to the radical expression, we have our final answer.

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