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

Apply Power Rule: Apply the power of a power rule. The power of a power rule states that (x^m)^n = x^(m*n). Therefore, we can simplify (3^a)^2 using this rule. (3^a)^2 = 3^(a*2) = 3^(2a)Compare to Answer Choices: Compare the simplified expression to the answer choices. We have simplified the expression to 3^(2a). Now we need to compare this to the answer choices to find the equivalent expression. (A) 9^2a is not equivalent because it suggests (9^2)^a which is 81^a, not 3^(2a). (B) 9^a is equivalent because 9 is 3^2, so 9^a is (3^2)^a which simplifies to 3^(2a). (C) 6^2a is not equivalent because it suggests (6^2)^a which is 36^a, not 3^(2a). (D) 6^a is not equivalent because it has a base of 6, not 3.Select Correct Answer: Select the correct answer. From the comparison in Step 2, we can see that the correct answer is (B) 9^a.

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Which of the following is equivalent to $\left(3^a\right)^2$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $9^{2a}$ $\newline$ (B) $9^{a}$ $\newline$ (C) $6^{2a}$ $\newline$ (D) $6^{a}$

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Math Problems

Algebra 1

Simplify radical expressions

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Q. Which of the following is equivalent to

\left(3^a\right)^2

\newline

Choose

1

answer:

\newline

(A)

9^{2a}

\newline

(B)

9^{a}

\newline

(C)

6^{2a}

\newline

(D)

6^{a}

Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(x^m)^n = x^{m*n}$ . Therefore, we can simplify $(3^a)^2$ using this rule. $\newline$ $(3^a)^2 = 3^{a*2} = 3^{2a}$
Compare to Answer Choices: Compare the simplified expression to the answer choices. $\newline$ We have simplified the expression to $3^{2a}$ . Now we need to compare this to the answer choices to find the equivalent expression. $\newline$ (A) $9^{2a}$ is not equivalent because it suggests $(9^2)^a$ which is $81^a$ , not $3^{2a}$ . $\newline$ (B) $9^a$ is equivalent because $9$ is $3^2$ , so $9^a$ is $(3^2)^a$ which simplifies to $3^{2a}$ . $\newline$ (C) $9^{2a}$ $1$ is not equivalent because it suggests $9^{2a}$ $2$ which is $9^{2a}$ $3$ , not $3^{2a}$ . $\newline$ (D) $9^{2a}$ $5$ is not equivalent because it has a base of $9^{2a}$ $6$ , not $9^{2a}$ $7$ .
Select Correct Answer: Select the correct answer. $\newline$ From the comparison in Step $2$ , we can see that the correct answer is (B) $9^a$ .