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Which of the following is equivalent to (3^(a))^(2) ? Choose 1 answer: (A) 9^(2a) (B) 9^(a) (c) 6^(a) (D) 6^(2a)

Which of the following is equivalent to (3a)2 \left(3^{a}\right)^{2} ?\newlineChoose 11 answer:\newline(A) 92a 9^{2 a} \newline(B) 9a 9^{a} \newline(C) 6a 6^{a} \newline(D) 62a 6^{2 a}

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Full solution

Q. Which of the following is equivalent to (3a)2 \left(3^{a}\right)^{2} ?\newlineChoose 11 answer:\newline(A) 92a 9^{2 a} \newline(B) 9a 9^{a} \newline(C) 6a 6^{a} \newline(D) 62a 6^{2 a}
  1. Apply Power of Power Rule: To simplify the expression (3a)2(3^{a})^{2}, we use the power of a power rule, which states that (xm)n=xmn(x^{m})^{n} = x^{mn}.\newlineSo, (3a)2=3a∗2=32a(3^{a})^{2} = 3^{a*2} = 3^{2a}.
  2. Simplify 32a3^{2a}: Now we need to simplify 32a3^{2a}. Since 32a3^{2a} is the same as (32)a(3^2)^a, we can calculate 323^2 which is 99. Therefore, 32a=(32)a=9a3^{2a} = (3^2)^a = 9^a. However, we need to be careful here because the exponent 2a2a applies to the base 33, not just to 323^2. So the correct simplification is 32a3^{2a}00, not 32a3^{2a}11.

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