SOLUTION: would you mind checking my work please? 324^1/4 over 4^-1/4 you would bring 4^-1/4 up to the numerator because you cannot have a negative exponent so you get 324^1/4 times 4

Algebra ->  Rational-functions -> SOLUTION: would you mind checking my work please? 324^1/4 over 4^-1/4 you would bring 4^-1/4 up to the numerator because you cannot have a negative exponent so you get 324^1/4 times 4      Log On


   

Question 818929: would you mind checking my work please?
324^1/4 over 4^-1/4
you would bring 4^-1/4 up to the numerator because you cannot have a negative exponent
so you get
324^1/4 times 4^1/4
and you simplify
to get 48 times the cubed root of 2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

Now, I could write it as root%284%2C324%2A4%29 ,
but I prefer to write it with the fractional exponent.
At this point, I start factoring.
I know that 4=2%5E2 ,
but I have to work a bit to factor 324 .
So I try dividing it by 2 and see that
324 ÷ 2 = 162 and 162 ÷ 2 = 81,
so 324=2%2A2%2A81=2%5E2%2A81 ,
and since I know that 81=9%5E2=3%5E4 ,
I can write the prime factorization as
324=2%5E2%2A3%5E4
So
= %28%282%2A3%29%5E4%29%5E%221%2F4%22=6%5E%284%2A%221%2F4%22%29=6%5E1=highlight%286%29 .
You may prefer to write it as
for short.
(I just wrote it as I thought about it, and as I calculated it with pencil and paper. With a calculator, I can calculate 324%2A4=1296,
and root%284%2C1296%29=sqrt%28sqrt%281296%29%29=6 , but I prefer to factor and use paper, because that way there is no chance of pressing the wrong key).