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# SAT Prep Question

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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 $$a-b$$?

Apr 2, 2019

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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?

Apr 2, 2019
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Thanks.

MemeLord  Apr 3, 2019