Algebra problem, please help?
The new school year has started and I am moving into Pre-Calculus. Today, our teacher gave us a review of Algebra 2 and I can't seem to remember anything. It sucks though since he didn't explain anything to us and told us to simply, "Remove the cobwebs from your brain." The review consisted of factoring, polynomials, and what I am the worst at, negative exponents. I came across a question that I didn't really understand and I thought it would be a really good idea to get some help on here. Anyway, the question is:
(-2x)^-4
I know you have to do something with reciprocals and such but I can't seem to remember the process in which I get there. Thanks for all the help!
Comments
The first step is to change its form to 1/((-2x)^4) because of the negative on the exponent. 1/((-2x)^4) is the same as 1/((-2x)(-2x)(-2x)(-2x)) which equals 1/(16x^4).
Explanation:
a^-b= 1/(a^b)
Therefore:
(-2x)^-4 = -1/(2x)^4
The minus sign was placed in front of the 1 instead of 2x. This minus sign is allowed to move around.
Whenever there is a negative sign in the exponent you just write it as a reciprocal.
(-2x)⁻⁴ = 1/(-2x)⁴ = 1/((-2)⁴ x⁴) = 1/(16x⁴)