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Write the following as a radical expression.

15^((5)/(6))

Write the following as a radical expression. $\newline$ $15^{\frac{5}{6}}$

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Evaluate integers raised to positive rational exponents

Full solution

Q. Write the following as a radical expression.

\newline

15^{\frac{5}{6}}

Understand as fraction: Understand the exponent as a fraction. The exponent $\frac{5}{6}$ can be broken down into two parts: the numerator $5$ , which is the power, and the denominator $6$ , which is the root.
Express as radical: Express the exponent as a radical. $\newline$ The expression $15^{\frac{5}{6}}$ can be written as the $6$ th root of $15$ raised to the $5$ th power. In radical form, this is written as $\sqrt[6]{15^5}$ with a small $6$ outside the radical to denote the $6$ th root.
Simplify radical expression: Simplify the radical expression. Since $15$ is not a perfect power of $6$ , we cannot simplify the radical further. Therefore, the expression remains as the $6$ th root of $15^5$ .

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