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!

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