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Which exponential expression is equivalent to
root(7)(b) ?
Choose 1 answer:
(A)
b^(7)
(B)
b^((1)/(7))
(c)
(1)/(b^(7))
(D)
(1)/(b^((1)/(7)))

Which exponential expression is equivalent to $\sqrt[7]{b}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $b^{7}$ $\newline$ (B) $b^{\frac{1}{7}}$ $\newline$ (C) $\frac{1}{b^{7}}$ $\newline$ (D) $\frac{1}{b^{\frac{1}{7}}}$

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Identify equivalent linear expressions

Full solution

Q. Which exponential expression is equivalent to

\sqrt[7]{b}

?

\newline

Choose

1

answer:

\newline

(A)

b^{7}

\newline

(B)

b^{\frac{1}{7}}

\newline

(C)

\frac{1}{b^{7}}

\newline

(D)

\frac{1}{b^{\frac{1}{7}}}

Understand Meaning of Seventh Root: Understand the meaning of the seventh root of $b$ . The seventh root of $b$ , denoted as $\sqrt[7]{b}$ , means a number that when raised to the power of $7$ gives $b$ .
Express in Exponential Form: Express the seventh root of $b$ in exponential form. $\newline$ The exponential form of a root can be written as a fraction. The seventh root of $b$ is equivalent to raising $b$ to the power of $\frac{1}{7}$ .
Match with Options: Match the exponential form with the given options. $\newline$ The correct exponential expression that matches $\sqrt[7]{b}$ is $b^{1/7}$ .
Identify Correct Answer: Identify the correct answer from the options. $\newline$ Option (A) $b^{7}$ is incorrect because it represents $b$ raised to the seventh power, not the seventh root. $\newline$ Option (C) $\frac{1}{b^{7}}$ is incorrect because it represents the reciprocal of $b$ raised to the seventh power. $\newline$ Option (D) $\frac{1}{b^{\left(\frac{1}{7}\right)}}$ is incorrect because it represents the reciprocal of the seventh root of $b$ . $\newline$ Option (B) $b^{\left(\frac{1}{7}\right)}$ is the correct answer because it represents the seventh root of $b$ .

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