SOLUTION: Simplify each expression. Assume that all variables are positive when they appear. A. 9(24)^(1/3) - (81)^(1/3) B. (32x)^(1/4) + (2x^5)^(1/4)

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Question 1208436: Simplify each expression. Assume that all variables are positive when they appear.
A. 9(24)^(1/3) - (81)^(1/3)
B. (32x)^(1/4) + (2x^5)^(1/4)


Found 3 solutions by Edwin McCravy, ikleyn, mccravyedwin:
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
A. 

Break all the base numbers down to primes:







Multiply exponents to raise powers to powers:





Add exponents of 3 to multiply powers of 3  



Factor out 34/3:
Divide powers of 3 by subtracting exponents:











Try this one on your own:

B. (32x)^(1/4) + (2x^5)^(1/4)

Edwin
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
Simplify each expression. Assume that all variables are positive when they appear.
(A) 9(24)^(1/3) - (81)^(1/3)
(B) (32x)^(1/4) + (2x^5)^(1/4)
~~~~~~~~~~~~~~~~~~~ 

(A)  9(24)^(1/3) = 9*(2^3*3)^(1/3) = 9*2*(3^(1/3)) = 18*(3^(1/3)).


     (81)^(1/3) = (3^4)^(1/3)) = 3*(3^(1/3)).


     THEREFORE,  9(24)^(1/3) - (81)^(1/3) = 18*(3^(1/3)) - 3*(3^(1/3)) = 15*(3^(1/3)).    ANSWER


     CHECK using a calculator.  Left side  9(24)^(1/3) - (81)^(1/3) = (using my MS EXCEL) = 21.63374355...

                                Right side  15*(3^(1/3)) = (using my MS EXCEL) = 21.63374355...


     Both values are equal, HENCE, the answer is confirmed.

Completed to the end.

----------------------

In his solution,  although it is long,  Edwin did not simplify the given expression to the end.

Therefore,  I came to make this job complete in a way as it  SHOULD  be done.


////////////////////////


Regarding part  B,  you write,  " Assume that all variables are positive when they appear. "

It is not an assumption,  which one can make or do not make.

This condition  x >= 0  describes the  DOMAIN,  where the whole expression is defined.

It is not defined if   x < 0.


So,  it would be more accurate mathematically to write  " simplify expression in its domain,  where it is defined. "


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


Dear visitor,  if you're confused about the post by @mccravyedwin,  it is Edwin making a joke this way.

In other words,  Edwin is in a good mood and agrees with me.

Maybe even repentant.



Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!

It depends on how you define the word "simplified".



requires only 4 digits to write.

Ikleyn's solution 

requires a whopping 5 digits.  J

Edwin
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