Question

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.

Answer 1

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

Answer 2

yes

Answer 3

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))

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

yes there was

Answer 8

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

Answer 9

oh yikes I overlooked that

Answer 10

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

Answer 11

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

Answer 12

Great I get coefficients of 1 3 and 27

Answer 13

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

Answer 14

now i wonder if we can go further...

Answer 15

cool that exactly where I am at the moment as well

Answer 16

oh I had -27^(-3)

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

ok so the exponents are not being multiplied in this case

Answer 21

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

Answer 22

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

Answer 23

when you multiply you add the exponents

Answer 24

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

Answer 25

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)

Answer 26

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

Answer 27

you don't need to change the denominator is 2

Answer 28

yw

Answer 29

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

Answer 30

got it

Answer 31

awesome!