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Which exponential expression is equivalent to
root(8)(y) ?
Choose 1 answer:
(A)
(1)/(y^((1)/(8)))
(B)
y^((1)/(8))
(c)
y^(8)
(D)
(1)/(y^(8))

Which exponential expression is equivalent to $\sqrt[8]{y}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{y^{\frac{1}{8}}}$ $\newline$ (B) $y^{\frac{1}{8}}$ $\newline$ (C) $y^{8}$ $\newline$ (D) $\frac{1}{y^{8}}$

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Identify equivalent linear expressions

Full solution

Q. Which exponential expression is equivalent to

\sqrt[8]{y}

?

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{y^{\frac{1}{8}}}

\newline

(B)

y^{\frac{1}{8}}

\newline

(C)

y^{8}

\newline

(D)

\frac{1}{y^{8}}

Understanding the $8$ th root of $y$ : Understand the meaning of the $8$ th root of $y$ . The $8$ th root of $y$ is the number that, when raised to the power of $8$ , gives $y$ . This can be written as $y^{(1/8)}$ .
Translating the $8$ th root into an exponential expression: Translate the $8$ th root into an exponential expression. $\newline$ The $8$ th root of $y$ is equivalent to raising $y$ to the power of $\frac{1}{8}$ , which is written as $y^{\frac{1}{8}}$ .
Matching the exponential expression with the given choices: Match the exponential expression with the given choices. $\newline$ The correct exponential expression that matches $y^{\frac{1}{8}}$ is option (B) $y^{\left(\frac{1}{8}\right)}$ .

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