OpenStudy (fanduekisses):

How do you factor and simplify this algebraic expression?

2 years ago
OpenStudy (fanduekisses):

\[(x+7)^{-1/5}-(x+7)^{-6/5}\]

2 years ago
OpenStudy (fanduekisses):

My skills are rusty lol

2 years ago
OpenStudy (fanduekisses):

1/5 is root 5 right? but if it's negative?

2 years ago
OpenStudy (anonymous):

that means the reciprocal

2 years ago
OpenStudy (anonymous):

if it's negative, it's in the denominator

2 years ago
OpenStudy (anonymous):

what @peachpi said put it in the denominator

2 years ago
OpenStudy (fanduekisses):

\[\frac{ 1 }{ \sqrt[5]{x+7} }\]

2 years ago
OpenStudy (anonymous):

oops i meant factor out the common factor of \[(x+7)^{-\frac{1}{5}}\] which is what you are asked to do

2 years ago
OpenStudy (anonymous):

so you'd be left with \[(x+7)^{\frac{ 1 }{ 5 }}(1-(x+7)^{6})\]

2 years ago
OpenStudy (fanduekisses):

there's a common factor?

2 years ago
OpenStudy (anonymous):

that's supposed to be ^-1/5

2 years ago
OpenStudy (anonymous):

\[(x+7)^{\frac{ -1 }{ 5 }}\] is the common factor as @satellite73 pointed out

2 years ago
OpenStudy (anonymous):

hold up I factored it wrong

2 years ago
OpenStudy (anonymous):

|dw:1432598749235:dw|

2 years ago