Factor and simplify the algebraic expression.
(x+7)^1/4 - (x+7)^5/4

Question

Factor and simplify the algebraic expression.
(x+7)^1/4 - (x+7)^5/4

anonymous · Answer

$$(x+7)^{\frac{1}{4}}-(x+7)^{\frac{5}{4}}$$
$$=(x+7)^{\frac{1}{4}}(1-(x+7)^{\frac{4}{4}})$$ is a start

anonymous · Answer

Isn't (x+7)^1/4 the GCF?

anonymous · Answer

then then next step, since $\frac{4}{4}=1$ is to rewrite as 
$$=(x+7)^{\frac{1}{4}}(1-(x+7))$$

anonymous · Answer

it is the GCF and that is why you factor it out

anonymous · Answer

so my original equation = what you just gave me?

anonymous · Answer

the "final answer" would be 
$$(x+7)^{\frac{1}{4}}(-x-6)$$ or 
$$-(x+6)(x+7)^{\frac{1}{4}}$$ sicnce $1-(x+7)=-x-6$

anonymous · Answer

But I thought that (1-(x+7)) = -x-7 because you distribute the negative and then the one makes it stay the same... right?