Home » ((frac{x^a}{x^b}))a + b by ((frac{x^{a + b}}{x^{a – b}}))(frac{a^2}{b})

((frac{x^a}{x^b}))a + b by ((frac{x^{a + b}}{x^{a – b}}))(frac{a^2}{b})

((frac{x^a}{x^b}))^{a + b} by ((frac{x^{a + b}}{x^{a – b}}))^{(frac{a^2}{b})}

A.
x^-a2
B.
x^b2
C.
x^{a2 – b2}
D.
(frac{1}{x^{a2 + b2}})
E.
x^{b2 – a2}

Correct Answer: Option D

Explanation

((frac{x^a}{x^b}))^{a + b} = ((frac{x^{a2 + ab}}{x^{b2 + ab}}))
= x^{a2 – b2}
{(frac{xa + b}{xa – b})} = x^{a + b – a + b}
= x^2b
= x^2a
= x^{a2 – b2}
= x^{b2 (div ) a2} = (frac{1}{x^text a2 + b2})