Select all the expressions that are equivalent to 12^2/2^2. Multi-select Choices: (A)1/6^-2 (B)6^2 (C)6 (D)6^0

Simplify expression: First, simplify the given expression $ \frac{12^2}{2^2} $ by calculating the squares and then dividing. $ \frac{12^2}{2^2} = \frac{144}{4} $Divide to simplify: Now, divide 144 by 4 to get the simplified result. $ \frac{144}{4} = 36 $Recognize equivalent value: Recognize that 36 is the same as $ 6^2 $. $ 36 = 6^2 $Evaluate given choices: Now, let's evaluate each of the given choices to see if they are equivalent to $ 6^2 $. (A) $ \frac{1}{6^{-2}} $ is equivalent to $ 6^2 $ because the negative exponent in the denominator means the base is reciprocated and squared, which is $ 6^2 $. (B) $ 6^2 $ is clearly equivalent to $ 6^2 $. (C) $ 6 $ is not equivalent to $ 6^2 $ because $ 6 = 6^1 $ and $ 6^1 \neq 6^2 $. (D) $ 6^0 $ is not equivalent to $ 6^2 $ because any non-zero number raised to the power of 0 is 1, so $ 6^0 = 1 $ and $ 1 \neq 6^2 $.

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Algebra 2

Simplify rational expressions

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Q. Select all the expressions that are equivalent to

12^2/2^2

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Multi-select Choices:

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(A)

1/6^{-2}

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(B)

6^2

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(C)

6

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(D)

6^0

Simplify expression: First, simplify the given expression $\frac{12^2}{2^2}$ by calculating the squares and then dividing. $\newline$ $\frac{12^2}{2^2} = \frac{144}{4}$
Divide to simplify: Now, divide $144$ by $4$ to get the simplified result. $\newline$ $\frac{144}{4} = 36$
Recognize equivalent value: Recognize that $36$ is the same as $6^2$ . $\newline$ $36 = 6^2$
Evaluate given choices: Now, let's evaluate each of the given choices to see if they are equivalent to $6^2$ . $\newline$ (A) $\frac{1}{6^{-2}}$ is equivalent to $6^2$ because the negative exponent in the denominator means the base is reciprocated and squared, which is $6^2$ . $\newline$ (B) $6^2$ is clearly equivalent to $6^2$ . $\newline$ (C) $6$ is not equivalent to $6^2$ because $6 = 6^1$ and $6^1 \neq 6^2$ . $\newline$ (D) $\frac{1}{6^{-2}}$ $0$ is not equivalent to $6^2$ because any non-zero number raised to the power of $0$ is $1$ , so $\frac{1}{6^{-2}}$ $2$ and $\frac{1}{6^{-2}}$ $3$ .