Select all the expressions that are equivalent to 12^2 / 6^2.
2^(-3)
2^(-5)
(2^(-2))^(-1)
2^2
Select all the expressions that are equivalent to 12^2 / 6^2
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Select all the expressions that are equivalent to 12^2 / 6^2.
2^(-3)
2^(-5)
(2^(-2))^(-1)
2^2
To simplify the expression ( frac{12^2}{6^2} ), we can start by rewriting it:
[
frac{12^2}{6^2} = left(frac{12}{6}right)^2 = 2^2
]
Now let’s evaluate the options given:
1. 2^(-3): This is not equal to ( 2^2 ).
2. 2^(-5): This is not equal to ( 2^2 ).
3. (2^(-2))^(-1): This simplifies to ( 2^{2} ) (using the power of a power rule: ((-2) times (-1) = 2)).
4. 2^2: This is directly equal to ( 2^2 ).
Thus, the expressions equivalent to ( frac{12^2}{6^2} ) are:
– (2^(-2))^(-1)
– 2^2
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