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Which exponential expression is equivalent to
root(9)(z) ?
Choose 1 answer:
(A)
z^(9)
(B)
(1)/(z^((1)/(9)))
(C)
(1)/(z^(9))
(D)
z^((1)/(9))

Which exponential expression is equivalent to $\sqrt[9]{z}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $z^{9}$ $\newline$ (B) $\frac{1}{z^{\frac{1}{9}}}$ $\newline$ (C) $\frac{1}{z^{9}}$ $\newline$ (D) $z^{\frac{1}{9}}$

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Identify equivalent linear expressions

Full solution

Q. Which exponential expression is equivalent to

\sqrt[9]{z}

?

\newline

Choose

1

answer:

\newline

(A)

z^{9}

\newline

(B)

\frac{1}{z^{\frac{1}{9}}}

\newline

(C)

\frac{1}{z^{9}}

\newline

(D)

z^{\frac{1}{9}}

Express $9$ th Root as Exponent: We need to express the $9$ th root of $z$ as an exponent. The $9$ th root of a number is the same as raising that number to the power of $\frac{1}{9}$ .
Write Expression for $9$ th Root of z: The expression for the $9$ th root of $z$ can be written as $z^{1/9}$ . This is because in general, the $n$ th root of a number $x$ is $x^{1/n}$ .
Analyze Given Options: Now we look at the options given to find which one matches our expression $z^{\frac{1}{9}}$ .
(A) $z^{9}$ is incorrect because it represents $z$ raised to the $9^{\text{th}}$ power, not the $9^{\text{th}}$ root of $z$ .
(B) $\frac{1}{z^{\frac{1}{9}}}$ is incorrect because it represents the reciprocal of the $9^{\text{th}}$ root of $z$ .
(C) $\frac{1}{z^{9}}$ is incorrect because it represents the reciprocal of $z$ raised to the $9^{\text{th}}$ power.
(D) $z^{\frac{1}{9}}$ is correct because it represents the $9^{\text{th}}$ root of $z$ .
Identify Correct Answer: The correct answer is (D) $z^{\frac{1}{9}}$ , which is equivalent to the $9$ th root of $z$ .

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