I have an SAT Prep question I've been trying to figure out for two days but I'm stumped. Can I get some help?
The problem is:
If \(\frac{x^{a^2}}{x^{b^2}}=x^16,x>1\) (that's (x^(a^2))/(x^(b^2))=x^16) and \(a+b=2\), then what is the value of \(a-b\)?
x ^(a^2-b^2) = x^(16)
So a^2 - b^2 = 16 a^2 - b^2 is a difference of squares
(a-b)(a+b) = 16 a+b is given as 2 sub this in
(a-b) (2) = 16
(a-b) = 8 cool?