Question

Please perform the indicated operation AND state the domain.
4x^(2/3)/5x^(1/2)
Thanks. Please perform the indicated operation AND state the domain.
4x^(2/3)/5x^(1/2)
Thanks. @Mathematics

Answer 1

Multiply the coefficients: 4 x 5 is 20 multiply the variables by adding the exponents: x^2/3(x^1/2) =x^7/6. So the result is 20x^7/6.
Now the domain: since you have x^1/2, you are taking an even root of x. In the set of real numbers you cannot take the square root of a negative number so the domain is x must be greater than or equal to 0.

Answer 2

Its actually division--sorry if that was unclear. My answer was 4x^(1/6)/5
The thing i dont understand is domain.

Answer 3

What is the square root of -4 greeneyes?

Answer 4

This has nothing to do with square roots...

Answer 5

Yes it does sweetheart because x^1/2 means the square root of x

Answer 6

(4/5)x^(1/6)

domain = (0, infinity)

because negative x=imaginary numbers

Answer 7

the simplification of 4x^(2/3) / 5x^(1/2) is simply (4/5) * x^( (2/3) - (1/2) )

Answer 8

\[\frac{4x^\frac{2}{3}}{5x^\frac{1}{2}}\]
domain is x>0
---------------------------------
\[\frac{4}{5} \cdot \frac{x^\frac{2}{3}}{x^\frac{1}{2}}=\frac{4}{5} \cdot x^{\frac{2}{3}-\frac{1}{2}}=\frac{4}{5}x^{\frac{4}{6}-\frac{3}{6}}=\frac{4}{5}x^\frac{1}{6}\]

Answer 9

mertsj is right
\[\sqrt{x}=x^\frac{1}{2}\]

Answer 10

I know the answer is 4x^(1/6)/5
the domain is all positive real #'s?

Answer 11

yea it's 0 inclusive. so it should actually be [0, infinity) (note the usage of bracket and not parenthesis)

Answer 12

\[\sqrt[a]{x^b}=x^\frac{b}{a}\]
yes domain is all positive real numbers
it doesn't include 0

Answer 13

NO. The domain is x > 0 because you cannot have the square root of a negative number and x^1/2 means the square root of x so x cannot be negative and it cannot be 0 because it is in the denominator

Answer 14

\[\frac{4x^\frac{2}{3}}{5 x^\frac{1}2}\] is the expression we are looking at

Answer 15

Yes and if x = 0 then the denominator is 0 and the expression is meaningless.

Answer 16

this expression equals \[\frac{4}{5}x^\frac{1}{6}\] as long as x does not equal 0

Answer 17

Or as long as x is not negative

Answer 18

You cannot have an even root of a negative root in the set of real numbers

Answer 19

I mean negative number

Answer 20

0 is inclusive because the x value is not in the denominator...

Answer 21

hey i feel on simplifying the expression we are having \[0.8 \times \sqrt[6]{x}\]
and as x is a variable so global minimum will be Zero

Answer 22

i know they have the same domain if x=0 is not in question

Answer 23

It is in the original expression. You cannot take something which is meaningless and make it meaningful by computing with it.

Answer 24

Franklin. x cannot be 0

Answer 25

x can be zero @ mertsj

Answer 26

so fronk you are saying
\[\frac{4}{5} \cdot \frac{0^\frac{2}{3}}{0^\frac{1}{2}} \text{ is a number that xeists}\]

Answer 27

x cannot be zero

Answer 28

It cannot.

Answer 29

why dont u guys simplify the whole expression

Answer 30

we did but you must consider the domain of the original expression

Answer 31

We have done that numerous times. How many times do you require?

Answer 32

(and yes mertsj I know they that the domains of both do not include the negatives) the two expression are = as long as we don't include x=0

Answer 33

see if u are going to simplify then also u will be having only original expressions value in the same proportion as it is

Answer 34

Well thanks for helping :P

Answer 35

I know this is an old question, and i'm just asking b/c i need to know by tomorrow and people dont usually answer me...So, can one of u help me find the domain for 5x^(2/3) and -9x^(2/3)? Thanks :)