Select all the expressions that are equivalent to 3⁻² · 4⁻²

To solve for expressions equivalent to (3^{-2} cdot 4^{-2}), we can rewrite it as follows:

1. (3^{-2} = frac{1}{3^2} = frac{1}{9})
2. (4^{-2} = frac{1}{4^2} = frac{1}{16})

Now, multiplying these together:

[

3^{-2} cdot 4^{-2} = frac{1}{9} cdot frac{1}{16} = frac{1}{144}

]

Next, let’s examine each option:

– 12⁴: This is equal to (20736), not equivalent.

– 12⁻⁴: This is (1/20736), not equivalent.

– 1/12²: Since (12^2 = 144), this equals (1/144), which is equivalent.

– 12⁻²: This is also (1/144), so it is equivalent.

Thus, the correct answers are 1/12² and 12⁻².

Keep practicing, and don’t hesitate to reach out if you have more questions!