Question

Vanessa and William are stuck simplifying radical expressions. Vanessa has to simplify the quantity of x to the four thirds power, over x to the five sixths power. William has to simplify the sixteenth root of the quantity of x times x to the third times x to the fourth. Using full sentences describe how to fully simplify Vanessa and William's expressions. Describe if Vanessa and William started with equivalent expressions or if they started with expressions that are not equal.

Answer 1

@whpalmer4

Answer 2

\[\frac{x^m}{x^n} = x^{m-n}\]

Answer 3

\[\sqrt[n]{x} = x^{\frac{1}n}\]

Answer 4

\[x^m*x^n = x^{n+m}\]I think that is all you need...

Answer 5

You have to simplify these 2 expressions : \[\frac{ x ^{\frac{ 4 }{ 3 }} }{ x ^{\frac{ 5 }{ 6 }} } and \sqrt[16]{x ^{8}}\]
You can use the properties palmer just wrote.

Answer 6

so @math&ing001 for the the first equation would \[x \frac{ 5 }{ 18 }\] be right

Answer 7

and for william the final answer would be \[x \frac{ 12 }{ 16 }\]

Answer 8

Check again, 4/5 - 5/6 is not equal to 5/18 !

Answer 9

Sorry 4/3 - 5/6*

Answer 10

And for William's radical expression use this : \[\sqrt[a]{x ^{b}}=x ^{\frac{ b }{ a }}\]
Good luck !

Answer 11

i thought you had to find the gcf

Answer 12

or least common factoe

Answer 13

Yes you do for adding fractions but you made a little mistake, show me the steps in your work, maybe we can find it.

Answer 14

\[x \frac{ 4 }{ 3 }\div x \frac{ 5 }{ 6}\]

Answer 15

\[\frac{ 20 }{ 18}-\frac{ 15 }{ 18 }\]

Answer 16

See that's the mistake. It's not 20 but 24
\[x ^{\frac{ 4 }{ 3 }-\frac{ 5 }{ 6 }}=x ^{\frac{ 24-15 }{ 18 }}\]

Answer 17

oh ok so it would be \[\frac{ 9 }{18}=\frac{ 1 }{ 2 }\]

Answer 18

Yep !

Answer 19

ok and what about the other equation

Answer 20

was my final answer for william was right

Answer 21

Nope, see the hint I gave above.

Answer 22

i thought i did it right because i thought you had to multiply the 3 and the 4

Answer 23

do i have to switch the number around

Answer 24

Use this property : \[\sqrt[a]{x ^{b}}=x ^{\frac{ b }{ a }}\]

Answer 25

i did already

Answer 26

Then how would you get 12/16 ?

Answer 27

because i thought you was suppose to multiple the 3 and the 4

Answer 28

am i not suppose to multiply the 3 and 4

Answer 29

This is William's expression :\[\sqrt[16]{x ^{8}}\] There's no 3 or 4 in it.

Answer 30

yes there is inside the radical it has an x*x^3*x^4

Answer 31

in the problem that im looking at it has that

Answer 32

Yeah, I kind of did that part for you. You're not supposed to multiply the 3 and 4, you add all the powers like this x*x^3*x^4=x^(1+3+4)

Answer 33

ohhh ok so it would be 8/16

Answer 34

which then equals to 1/2 as well

Answer 35

Exactly :)

Answer 36

for the first equation is the answer x^1/2 or just 1/2?

Answer 37

\[\frac{x^{4/3}}{x^{5/6}}=x^{(4/3-5/6)}=\]

now, how would you get from that to the answer being simply \(1/2\), when you do not know anything about the value of \(x\)?