If #x^(a^2)/x^(b^2)=x^16#, x>1, and a+b=2, what is the value of a-b?

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Answer 1 · 2016-11-20T04:41:31

#a - b = 8#.

By the quotient rule of exponents #a^n ÷ a^m = a^(n - m)#

#x^(a^2 - b^2) = x^16#

#a^2 - b^2 = 16#

#(a + b)(a - b) = 16#

We know that #a + b = 2#.

#2(a - b) = 16#

#a - b = 8#

Hopefully this helps!