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Which exponential expression is equivalent to
root(8)(z^(7)) ?
Choose 1 answer:
(A)
(z^(7))/(z^(8))
(B)
z^((8)/(7))
(C)
z^((7)/(8))
(D)
(z^(8))/(z^(7))

Which exponential expression is equivalent to $\sqrt[8]{z^{7}}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{z^{7}}{z^{8}}$ $\newline$ (B) $z^{\frac{8}{7}}$ $\newline$ (C) $z^{\frac{7}{8}}$ $\newline$ (D) $\frac{z^{8}}{z^{7}}$

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Identify equivalent linear expressions

Full solution

Q. Which exponential expression is equivalent to

\sqrt[8]{z^{7}}

?

\newline

Choose

1

answer:

\newline

(A)

\frac{z^{7}}{z^{8}}

\newline

(B)

z^{\frac{8}{7}}

\newline

(C)

z^{\frac{7}{8}}

\newline

(D)

\frac{z^{8}}{z^{7}}

Understand the meaning: Understand the meaning of the $8$ th root of $z$ raised to the $7$ th power. $\newline$ The $8$ th root of $z^{7}$ can be written as $(z^{7})^{\frac{1}{8}}$ .
Apply exponent rule: Apply the exponent rule for powers of powers. $\newline$ When you have a power raised to another power, you multiply the exponents. In this case, we have $z$ raised to the $7^{\text{th}}$ power, and then taking the $8^{\text{th}}$ root, which is the same as raising it to the power of $1/8$ . $\newline$ $(z^{7})^{1/8} = z^{7 \times 1/8}$
Perform multiplication of exponents: Perform the multiplication of the exponents. $\newline$ $7 \times \frac{1}{8} = \frac{7}{8}$ $\newline$ So, $(z^{7})^{\frac{1}{8}} = z^{\frac{7}{8}}$ .
Match result with choices: Match the result with the given choices. $\newline$ The expression $z^{\frac{7}{8}}$ matches choice (C).

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