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 \(a-b\)?

MemeLord Apr 2, 2019

#1**+2 **

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?

ElectricPavlov Apr 2, 2019