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Which exponential expression is equivalent to
root(5)(c) ?
Choose 1 answer:
(A)
c^(5)
(B)
(1)/(c^(5))
(c)
(1)/(c^((1)/(5)))
(D)
(1)/(c^(5))

Which exponential expression is equivalent to $\sqrt[5]{c}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $c^{5}$ $\newline$ (B) $\frac{1}{c^{5}}$ $\newline$ (C) $\frac{1}{c^{\frac{1}{5}}}$ $\newline$ (D) $\frac{1}{c^{5}}$

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Identify equivalent linear expressions

Full solution

Q. Which exponential expression is equivalent to

\sqrt[5]{c}

?

\newline

Choose

1

answer:

\newline

(A)

c^{5}

\newline

(B)

\frac{1}{c^{5}}

\newline

(C)

\frac{1}{c^{\frac{1}{5}}}

\newline

(D)

\frac{1}{c^{5}}

Understand the meaning: Understand the meaning of the $5$ th root of $c$ . The $5$ th root of $c$ is the number that, when raised to the power of $5$ , gives $c$ . This can be written as $c^{(1/5)}$ .
Match with choices: Match the $5^{\text{th}}$ root of $c$ with the given choices. $\newline$ (A) $c^{5}$ is $c$ raised to the power of $5$ , not the $5^{\text{th}}$ root of $c$ . $\newline$ (B) $\frac{1}{c^{5}}$ is the reciprocal of $c$ raised to the power of $5$ , not the $5^{\text{th}}$ root of $c$ . $\newline$ (C) $c$ $2$ is the reciprocal of the $5^{\text{th}}$ root of $c$ , which is the correct expression for the $5^{\text{th}}$ root of $c$ . $\newline$ (D) $\frac{1}{c^{5}}$ is repeated from choice (B) and is incorrect for the same reason.

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