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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 (c7)5 (\sqrt[7]{c})^{5} ?\newlineChoose 11 answer:\newline(A) c57 c^{\frac{5}{7}} \newline(B) c75 c^{\frac{7}{5}} \newline(C) c5c7 \frac{c^{5}}{c^{7}} \newline(D) c7c5 \frac{c^{7}}{c^{5}}

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Full solution

Q. Which exponential expression is equivalent to (c7)5 (\sqrt[7]{c})^{5} ?\newlineChoose 11 answer:\newline(A) c57 c^{\frac{5}{7}} \newline(B) c75 c^{\frac{7}{5}} \newline(C) c5c7 \frac{c^{5}}{c^{7}} \newline(D) c7c5 \frac{c^{7}}{c^{5}}
  1. Given Expression: We are given the expression (c7)5(\sqrt[7]{c})^{5} and need to find an equivalent exponential expression.\newlineThe c7\sqrt[7]{c} can be written as c17c^{\frac{1}{7}} because the 77th root of cc is the same as raising cc to the power of 17\frac{1}{7}.
  2. Rewriting the Expression: Now, we need to apply the exponent of 55 to the expression c(1/7)c^{(1/7)}. Using the power of a power rule (am)n=am∗n(a^{m})^{n} = a^{m*n}, we multiply the exponents together. So, $(c^{(\(1\)/\(7\))})^{\(5\)} = c^{((\(1\)/\(7\))*\(5\))}.
  3. Applying the Exponent: Perform the multiplication of the exponents: \((\frac{1}{7})\times 5 = \frac{5}{7}\).\(\newline\)Therefore, \((c^{\frac{1}{7}})^5 = c^{\frac{5}{7}}\).
  4. 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.

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