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Which exponential expression is equivalent to
root(6)(t) ?
Choose 1 answer:
(A)
t^(6)
(B)
(1)/(t^((1)/(6)))
(c)
t^((1)/(6))
(D)
(1)/(t^(6))

Which exponential expression is equivalent to $\sqrt[6]{t}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $t^{6}$ $\newline$ (B) $\frac{1}{t^{\frac{1}{6}}}$ $\newline$ (C) $t^{\frac{1}{6}}$ $\newline$ (D) $\frac{1}{t^{6}}$

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Identify equivalent linear expressions

Full solution

Q. Which exponential expression is equivalent to

\sqrt[6]{t}

?

\newline

Choose

1

answer:

\newline

(A)

t^{6}

\newline

(B)

\frac{1}{t^{\frac{1}{6}}}

\newline

(C)

t^{\frac{1}{6}}

\newline

(D)

\frac{1}{t^{6}}

Understanding the sixth root of $t$ : Understand the meaning of the sixth root of $t$ . The sixth root of $t$ , denoted as $\sqrt[6]{t}$ , means a number which when raised to the power of $6$ gives $t$ .
Expressing the sixth root of $t$ in exponential form: Express the sixth root of $t$ in exponential form. $\newline$ The exponential form of a root can be expressed as a fractional exponent. The sixth root of $t$ is the same as $t$ raised to the power of $\frac{1}{6}$ .
Matching the correct exponential expression: Match the correct exponential expression. $\newline$ From the given options, we need to find the one that correctly represents $t$ raised to the power of $\frac{1}{6}$ . $\newline$ (A) $t^{6}$ is $t$ raised to the power of $6$ , which is not correct. $\newline$ (B) $\frac{1}{t^{\left(\frac{1}{6}\right)}}$ is the reciprocal of $t$ raised to the power of $\frac{1}{6}$ , which is not correct. $\newline$ (C) $t^{\left(\frac{1}{6}\right)}$ is $t$ raised to the power of $\frac{1}{6}$ , which is correct. $\newline$ (D) $\frac{1}{6}$ $1$ is the reciprocal of $t$ raised to the power of $6$ , which is not correct.

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