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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
 #1
avatar+24889 
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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?   cheeky

 Apr 2, 2019
 #2
avatar+81 
+2

Thanks.

MemeLord  Apr 3, 2019

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