Question

Stuck on a math: Fraction exponent factoring and simplifying.

Answer 1

Step-by-step explanation:

(x+2)^(-1/5) - (x+2)^(-6/5)

Factor out (x+2)^(-1/5):

(x+2)^(-1/5) [ 1 - (x+2)^(-5/5) ]

(x+2)^(-1/5) [ 1 - (x+2)^-1 ]

(x+2)^(-1/5) [ 1 - 1/(x+2) ]

Common denominator:

(x+2)^(-1/5) [ (x+2)/(x+2) - 1/(x+2) ]

(x+2)^(-1/5) [ (x+2-1)/(x+2) ]

(x+2)^(-1/5) [ (x+1)/(x+2) ]

Answer 2

$(x+2)^{-\frac{1}{5}}-(x+2)^{-\frac{6}{5}}$

$\dfrac{1}{(x+2)^{\frac{1}{5}}}-\dfrac{1}{(x+2)^{\frac{6}{5}}}$

$\dfrac{1}{\sqrt[5]{x+2}}-\dfrac{1}{(x+2)\sqrt[5]{x+2}}$

$\boxed{\dfrac{x+1}{\sqrt[5]{x+2}\cdot(x+2)}}$

Hope this helps.

r3t40