Select all the expressions that are equivalent to 12^2 / 6^2

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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