Simplify and write in equivalent form with positive exponents.
(4x^-2)^-2

So I have my answer, but want to make sure i am on the right track.

Question

Simplify and write in equivalent form with positive exponents.
(4x^-2)^-2

So I have my answer, but want to make sure i am on the right track.

lgbasallote · Answer

what's your answer?

anonymous · Answer

my answer is -16x^4

lgbasallote · Answer

close...very..

lgbasallote · Answer

$$\Large (4x^{-2})^{-2} \implies \frac{1}{(4x^{-2})^2} \implies \frac{1}{16x^{-4}} \implies \frac{x^4}{16}$$

lgbasallote · Answer

do you get it?

anonymous · Answer

what I am having trouble understanding is why we add a one in the numberator. Are we dividing?

lgbasallote · Answer

well i cant just leave the numerator blank can i.. $$\Large \frac{}{(4x^{-2})^2}$$
that looks awkward

lgbasallote · Answer

that's why there's a 1 in the numerator

lgbasallote · Answer

because 1 is like the identity number

anonymous · Answer

ok I guess that wouldn't make sense lol.

lgbasallote · Answer

anything you multiply by 1 is the number itself

lgbasallote · Answer

maybe this can help you $$\huge a^{-m} = \frac{1}{a^m}$$
that means if a number has a negative exponent then you put it in the denominator

anonymous · Answer

ok, so I do understand that anything multiplied by one is the same number.

lgbasallote · Answer

so what dont you understand?

anonymous · Answer

no, actually when you gave me that example, it does make sense. (if I can just remember to do this myself with similar problems.) thank you

lgbasallote · Answer

ahh. welcome ^_^