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

Nov 20, 2016

$a - b = 8$.

#### Explanation:

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

${x}^{{a}^{2} - {b}^{2}} = {x}^{16}$

${a}^{2} - {b}^{2} = 16$

$\left(a + b\right) \left(a - b\right) = 16$

We know that $a + b = 2$.

$2 \left(a - b\right) = 16$

$a - b = 8$

Hopefully this helps!