Select all the expressions that are equivalent to 3⁻² · 4⁻².
12⁴
12⁻⁴
1/12²
12⁻²
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Select all the expressions that are equivalent to 3⁻² · 4⁻².
12⁴
12⁻⁴
1/12²
12⁻²
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!