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

To solve ( frac{12^2}{6^2} ), we start by simplifying that expression:

1. Recognize that ( frac{12^2}{6^2} = left( frac{12}{6} right)^2 ).
2. Calculate ( frac{12}{6} = 2 ).
3. Therefore, ( frac{12^2}{6^2} = 2^2 ).

Now let’s evaluate the options given:

– ( 2^{-3} ) is not equivalent to ( 2^2 ).

– ( 2^{-5} ) is not equivalent to ( 2^2 ).

– ( (2^{-2})^{-1} = 2^{2} ) is equivalent to ( 2^2 ).

– ( 2^2 ) is definitely equivalent to ( 2^2 ).

So the expressions that are equivalent to ( frac{12^2}{6^2} ) are:

– ( (2^{-2})^{-1} )

– ( 2^2 )

In summary, the correct answers are ( (2^{-2})^{-1} ) and ( 2^2 ).