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Write the following as an exponential expression.
root(5)(a^(2))

Write the following as an exponential expression. $\newline$ $\sqrt[5]{a^{2}}$

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Roots of integers

Full solution

Q. Write the following as an exponential expression.

\newline

\sqrt[5]{a^{2}}

Understand Relationship: Understand the relationship between radical and exponential forms. $\newline$ The $n$ th root of a number can be expressed as that number raised to the power of $1/n$ . In this case, we have the $5$ th root of $a^2$ , which can be written as $(a^2)^{1/5}$ .
Apply Exponent Rule: Apply the exponent rule. $\newline$ When raising a power to a power, you multiply the exponents. So, $(a^2)^{\frac{1}{5}}$ becomes $a^{2\cdot\frac{1}{5}}$ , which simplifies to $a^{\frac{2}{5}}$ .
Write Final Answer: Write the final answer. $\newline$ The exponential expression equivalent to the $5^{\text{th}}$ root of $a^2$ is $a^{(2/5)}$ .

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