Destinyyyy
  • Destinyyyy
Help with rational exponents and Find all the real and complex roots..
Mathematics
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Destinyyyy
  • Destinyyyy
Help with rational exponents and Find all the real and complex roots..
Mathematics
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
OKAY
Destinyyyy
  • Destinyyyy
4x ^3/2 -12=0
Destinyyyy
  • Destinyyyy
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anonymous
  • anonymous
MAKE SURE YOU ISOLATE THE TERM WITH X THEN USE LOG
freckles
  • freckles
don't think you need log
anonymous
  • anonymous
THEN WE DO NOT, LN
Destinyyyy
  • Destinyyyy
4x ^3/2 =12 x^3/2 = 3
Destinyyyy
  • Destinyyyy
I have no clue what log is
freckles
  • freckles
raise both sides to (2/3) power
anonymous
  • anonymous
OH i THOUGHT THAT WAS X IN THE EXPONENT HAHA MY BAD
Destinyyyy
  • Destinyyyy
x= 3 correct?
freckles
  • freckles
\[x^{\frac{3}{2}}=3 \\ x^{\frac{3}{2} \cdot \frac{2}{3}}=3^{\frac{2}{3}}\]
anonymous
  • anonymous
YOUR RATIONAL EXPONENT MAY BE REWRITTEN AS RADICALS
Destinyyyy
  • Destinyyyy
Yeah.. Then the x is alone. And 3 *3=9 divide that by 3 = 3
anonymous
  • anonymous
nooooo lol not like that
Destinyyyy
  • Destinyyyy
Then what?
anonymous
  • anonymous
rewrite it as cube root of 9
Destinyyyy
  • Destinyyyy
As in 9*9*9 ?
freckles
  • freckles
no cube root and cube are different terms
anonymous
  • anonymous
radical
anonymous
  • anonymous
https://www.mathsisfun.com/definitions/radical.html
Destinyyyy
  • Destinyyyy
So confused
freckles
  • freckles
cube of 9 is 9*9*9 but cube root of 9 means \[\sqrt[3]{9}\]
Destinyyyy
  • Destinyyyy
Oh thats what your asking
anonymous
  • anonymous
read the content of this link https://www.mathsisfun.com/definitions/radical.html
Destinyyyy
  • Destinyyyy
I have 3^ square root 9 written down already... Whats the next step?
freckles
  • freckles
\[x^{\frac{3}{2}}=3 \\ x^{\frac{3}{2} \cdot \frac{2}{3}}=3^{\frac{2}{3}} \\ x^{1}=3^\frac{2}{3} \\ x=3^{\frac{2}{3}} \\ x=(3^2)^\frac{1}{3} \] this is how he got cube root of 9 @Destinyyyy
freckles
  • freckles
nothing else really to do
Destinyyyy
  • Destinyyyy
Yes I know that.. Thats the final part? I thought there was more?
Destinyyyy
  • Destinyyyy
So the answer is -- 3^ square root 9
freckles
  • freckles
no not \[3^{\sqrt{9}}\]
freckles
  • freckles
cube root of 9 means \[\sqrt[3]{9}\]
Destinyyyy
  • Destinyyyy
Thats no what I mean
Destinyyyy
  • Destinyyyy
Yeah thats what im saying the 3 up top and square root 9
freckles
  • freckles
\[x^\frac{b}{a}=\sqrt[a]{x^{b}}\]
Destinyyyy
  • Destinyyyy
So thats the answer?
freckles
  • freckles
you can not do anything with the answer other than what we have already done
freckles
  • freckles
unless you are allowed to approximate
Destinyyyy
  • Destinyyyy
Okay
Destinyyyy
  • Destinyyyy
(x-3)^ 2/3 =25
Destinyyyy
  • Destinyyyy
x-3= 25 ^3/2
Destinyyyy
  • Destinyyyy
Since the 25 is now square root 25 do I change it to 5 and then times it by 3?
freckles
  • freckles
you mean write it as 5^3 ?
freckles
  • freckles
5^3 is not the same as 5(3)
Destinyyyy
  • Destinyyyy
I know.. Im saying 5*5*5
freckles
  • freckles
\[x-3=25^\frac{3}{2} \\ x-3=(25^\frac{1}{2})^3 \\ x-3=5^3 \]
freckles
  • freckles
yes that's right then
Destinyyyy
  • Destinyyyy
x-3= 125
Destinyyyy
  • Destinyyyy
So I ignore the 2??
freckles
  • freckles
what 2?
Destinyyyy
  • Destinyyyy
from 3/2
freckles
  • freckles
you did the square of 25 already you already used the 1/2 part
freckles
  • freckles
then you were left with 5^3 which is 5*5*5 which is 125
Destinyyyy
  • Destinyyyy
Ohhh... So x= 128
freckles
  • freckles
yeah you did it! :)
Destinyyyy
  • Destinyyyy
Okay :) Find all the real and complex roots. x^4 -12x^2 +27 =0

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