Select all of the expressions that are equivalent to 323−2

Question

Responses

3−4
3 to the negative 4 power

34
3

-12
-12

181
1 over 81

81
81

12
12

Answer 1

To simplify the expression \( 3^{2 - 4} \), we can break it down as follows:

1. Calculate \( 2 - 4 \): \[ 2 - 4 = -2 \]

2. Rewrite the expression: \[ 3^{2 - 4} = 3^{-2} \]

Next, let's analyze the equivalent forms of \( 3^{-2} \):

• \( 3^{-4} \): This expression is equivalent to \( \frac{1}{3^4} \), which is not equivalent to \( 3^{-2} \).
• \( 34 \): This seems to be a typographical error (it is likely meant to be \( 3^4 \)), and \( 3^4 = 81 \) is not equivalent.
• \( 3 \): This is simply \( 3^1 \), which is not equal to \( 3^{-2} \).
• \( -12 \): This is clearly not equivalent.
• \( 181 \): This is \( \frac{1}{81} \) which corresponds to \( 3^{-4} \), not \( 3^{-2} \).
• \( 81 \): This is \( 3^4 \) and not equal.
• \( 12 \): This is clearly not equivalent.

The correct equivalent forms of \( 3^{-2} \) would be:

• \( \frac{1}{3^2} = \frac{1}{9} \) (but this option is not listed).

Thus, the answer from the available options includes none of the expressions being equivalent to \( 3^{-2} \).

If we had the option \( \frac{1}{9} \), that would be the equivalent expression we're looking for, but from the provided responses no valid expressions are equivalent to \( 3^{-2} \).