Question

Simplify the given expression to radical form, justify each step by identifying the properties of rational exponents used.

Answer 1

@FutureMathProfessor

Answer 2

start by subtracting the exponents
\[\frac{2}{3}-\frac{4}{9}\]

Answer 3

you have to find the lowest common denominator so
2/18-4/18
-2/18?

Answer 4

@satellite73 is that right? what next?

Answer 5

@phi

Answer 6

to change the denominator, you multiply it by whatever number you want. But you have to do the same thing to the top.

try again

Answer 7

2*2/3*3
4*2/9*2
4/9 and 8/18

Answer 8

the 8/18 is ok

but you want to change 2/3 to x/18 (you want an 18 in the bottom to match the other fraction)
you should see you must multiply the 3 by 6 to get 18. that means *do the same to the top*

Answer 9

12/18 and 8/18

Answer 10

because 6*2

Answer 11

now you are in business

Answer 12

haha :D

Answer 13

is that the final answer?

Answer 14

What do i do next? I don't know how to simplify both answers into radical form

Answer 15

do what satellite said start by subtracting the exponents

Answer 16

4/0

Answer 17

4?

Answer 18

4/18

Answer 19

4/18 = 2/9

Answer 20

that is the exponent of x

so x^(2/9)

Answer 21

btw, you could have used a common denominator of 9. the bottom fraction is already ok.
the top could be changed by multiplying top and bottom by 3

but it does not matter much... 18 works fine

Answer 22

Thank you so much

Answer 23

so in radical form it would be 9√x2

Answer 24

if you use the equation editor, you could write it properly. that should be a "little" 9
\[ \sqrt[9]{x^2} \]

Answer 25

i did it on microsoft word with superscript and i copy and pasted it here but it didn't work

Answer 26

how do i get the equation editor?

Answer 27

the button in the lower left of the input area here.

Answer 28

Thanks