- anonymous

I am sure there is someone here that can easily tackle this problem! Factor: 3x^(-1/2)+9x^91/2)-81^(-3/2)
I panic when I see negative fractional exponents! And my factoring skills are weak at best If you can explain any of the steps or the way you think about the problem I would greatly appreciate the advice.

- chestercat

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- anonymous

\[ 3x^{\frac{-1}{2}}+9x^{\frac{1}{2}}-81^{\frac{-3}{2}}\] like this?

- anonymous

yes

- anonymous

I was thinking that an x^(1/2) If 81x^(-3/2) could be rewritten as 81x(-3(1/2)) and 3x(-1/2) could be rewritten as 3x^(-1(1/2))

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## More answers

- anonymous

i can write out what this means without negative exponents, but i cannot see how to factor it

- anonymous

oops that an x^(1/2) could be factored out *

- anonymous

oh wait, is there an x in the last term?

- anonymous

yes there was

- anonymous

\[3x^{\frac{-1}{2}}+9x^{\frac{1}{2}}-81x^{\frac{-3}{2}}\]

- anonymous

oh yikes I overlooked that

- anonymous

good catch. I looked over it so quickly the first time I missed the omission.

- anonymous

ok that is a whole different story. first off you can factor a 3 out of each term, then also perhaps an
\[x^{\frac{1}{2}}\] if you like. lets try it

- anonymous

Great I get coefficients of 1 3 and 27

- anonymous

\[3x^{\frac{1}{2}}(x^{-1}+3+27x^{-2})\]

- anonymous

now i wonder if we can go further...

- anonymous

cool that exactly where I am at the moment as well

- anonymous

oh I had -27^(-3)

- anonymous

no i think it is
\[27x^{-2}\]

- anonymous

because
\[\frac{-3}{2}-\frac{1}{2}=-2\]

- anonymous

i cannot see how to factor the second part, so i think you are done at that step

- anonymous

ok so the exponents are not being multiplied in this case

- anonymous

I was thinking it was -27x^(-3(1/2))

- anonymous

sorry i was off by a minus sign, should be
\[-27x^{-2}\]

- anonymous

when you multiply you add the exponents

- anonymous

so
\[3x^{\frac{1}{2}}\times -27x^{-2}=-81x^{\frac{1}{2}+(-2)}=-81x^{-\frac{3}{2}}\] which is what you want

- anonymous

ok I think I see how that works so x^(1/2)x^-2(2/2) = x^(1/2)x^(-4/4) or x^(-3/2)

- anonymous

Thank you so much for your help! This really helped clarify the concept for me.

- anonymous

you don't need to change the denominator is 2

- anonymous

yw

- anonymous

oops meant (-2(2/2) = (-4/2)

- anonymous

got it

- anonymous

awesome!

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