Which exponential expression is equivalent to (root(7)(c))^(5) ? Choose 1 answer: (A) c^((5)/(7)) (B) (7)/(c^(5)) (C) (c^(5))/(c^(7)) (D) (c^(7))/(c^(5))

Given Expression: We are given the expression (root(7)(c))^(5) and need to find an equivalent exponential expression. The root(7)(c) can be written as c^(1/7) because the 7th root of c is the same as raising c to the power of 1/7.Rewriting the Expression: Now, we need to apply the exponent of 5 to the expression c^(1/7). Using the power of a power rule (a^(m))^n = a^(m*n), we multiply the exponents together. So, (c^(1/7))^5 = c^((1/7)*5).Applying the Exponent: Perform the multiplication of the exponents: (1/7)*5 = 5/7. Therefore, (c^(1/7))^5 = c^(5/7).Multiplying the Exponents: Now we compare the result c^(5/7) with the given answer choices. (A) c^((5)/(7)) matches our result. (B) (7)/(c^(5)), (C) (c^(5))/(c^(7)), and (D) (c^(7))/(c^(5)) do not match our result.

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Which exponential expression is equivalent to
(root(7)(c))^(5) ?
Choose 1 answer:
(A)
c^((5)/(7))
(B)
(7)/(c^(5))
(C)
(c^(5))/(c^(7))
(D)
(c^(7))/(c^(5))

Which exponential expression is equivalent to $(\sqrt[7]{c})^{5}$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $c^{\frac{5}{7}}$ $\newline$ (B) $c^{\frac{7}{5}}$ $\newline$ (C) $\frac{c^{5}}{c^{7}}$ $\newline$ (D) $\frac{c^{7}}{c^{5}}$

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Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. Which exponential expression is equivalent to

(\sqrt[7]{c})^{5}

\newline

Choose

1

answer:

\newline

(A)

c^{\frac{5}{7}}

\newline

(B)

c^{\frac{7}{5}}

\newline

(C)

\frac{c^{5}}{c^{7}}

\newline

(D)

\frac{c^{7}}{c^{5}}

Given Expression: We are given the expression $(\sqrt[7]{c})^{5}$ and need to find an equivalent exponential expression. $\newline$ The $\sqrt[7]{c}$ can be written as $c^{\frac{1}{7}}$ because the $7$ th root of $c$ is the same as raising $c$ to the power of $\frac{1}{7}$ .
Rewriting the Expression: Now, we need to apply the exponent of $5$ to the expression $c^{(1/7)}$ . Using the power of a power rule $(a^{m})^{n} = a^{m*n}$ , we multiply the exponents together. So, $(c^{($1$/$7$)})^{$5$} = c^{(($1$/$7$)*$5$)}.
Applying the Exponent: Perform the multiplication of the exponents: $(\frac{1}{7})\times 5 = \frac{5}{7}$.$\newline$Therefore, $(c^{\frac{1}{7}})^5 = c^{\frac{5}{7}}$.
Multiplying the Exponents: Now we compare the result $c^{\frac{5}{7}}$ with the given answer choices.$\newline$(A) $c^{\left(\frac{5}{7}\right)}$ matches our result.$\newline$(B) $\frac{7}{c^{5}}$, (C) $\frac{c^{5}}{c^{7}}$, and (D) $\frac{c^{7}}{c^{5}}$ do not match our result.