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Which exponential expression is equivalent to (root(7)(a))^(2) ? Choose 1 answer: (A) a^((7)/(2)) (B) a^((2)/(7)) (C) (a^(7))/(a^(2)) (D) (a^(2))/(a^(7))

Which exponential expression is equivalent to (a7)2 (\sqrt[7]{a})^{2} ?\newlineChoose 11 answer:\newline(A) a72 a^{\frac{7}{2}} \newline(B) a27 a^{\frac{2}{7}} \newline(C) a7a2 \frac{a^{7}}{a^{2}} \newline(D) a2a7 \frac{a^{2}}{a^{7}}

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Full solution

Q. Which exponential expression is equivalent to (a7)2 (\sqrt[7]{a})^{2} ?\newlineChoose 11 answer:\newline(A) a72 a^{\frac{7}{2}} \newline(B) a27 a^{\frac{2}{7}} \newline(C) a7a2 \frac{a^{7}}{a^{2}} \newline(D) a2a7 \frac{a^{2}}{a^{7}}
  1. Problem Understanding: Let's first understand the problem. We need to find an equivalent exponential expression for (a7)2(\sqrt[7]{a})^2.
  2. Rewriting the Expression: The 77th root of aa can be written as a(1/7)a^{(1/7)}. So, (a7)2(\sqrt[7]{a})^2 can be rewritten as (a(1/7))2(a^{(1/7)})^2.
  3. Simplifying the Expression: Using the power of a power rule, which states that (am)n=a(m∗n)(a^m)^n = a^{(m*n)}, we can simplify (a(1/7))2(a^{(1/7)})^2 to a((1/7)∗2)a^{((1/7)*2)}.
  4. Calculating the Exponent: Now, we calculate (17)⋅2(\frac{1}{7})\cdot 2 which equals 27\frac{2}{7}. So, (a17)2(a^{\frac{1}{7}})^2 simplifies to a27a^{\frac{2}{7}}.
  5. Matching the Result: Comparing our result with the given choices, we find that a27a^{\frac{2}{7}} matches choice (B) a(27)a^{\left(\frac{2}{7}\right)}.

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