Question

Help please?

Answer 1

I used to remember how to do these.. but it's been a long time so I'm going to link a person who's likely to remember and is able to teach it very well @jim_thompson5910

Answer 2

First we'll use this rule


\[\Large \frac{\sqrt[n]{A}}{\sqrt[n]{B}} = \sqrt[n]{\frac{A}{B}}\]


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Using that rule, we go from this


\[\Large \frac{\sqrt[4]{32x^{11}y^{15}}}{\sqrt[4]{2x^3y^{-2}}}\]


to this


\[\Large \sqrt[4]{\frac{32x^{11}y^{15}}{2x^3y^{-2}}}\]

Answer 3

ahh i knew it was something like that. so can i divide 32/2?

Answer 4

which is what?

Answer 5

16. and for the variables i just subtract? so x^11-3 and y^15-(-2)?

Answer 6

so would it be 2x^8y^17? @jim_thompson5910

Answer 7

Sorry this site is being buggy

Answer 8

but yeah, you subtract the exponents for the corresponding variables

Answer 9

32/2 = 16, so you should have this so far

\[\Large \sqrt[4]{16x^{8}y^{17}}\]

Answer 10

it said that my answer was wrong though:c i know for the fact that 2^4=16

Answer 11

What's your next move?

Answer 12

if i square root 16 it would be 4? so do i just write "4(x^8y^17)^(1/4)?

Answer 13

or 4x^2(x^2y^17)^(1/4)? @jim_thompson5910

Answer 14

we have this

\[\Large \sqrt[4]{16x^{8}y^{17}}\]

Answer 15

we then rewrite that as

\[\Large \left(16x^{8}y^{17}\right)^{1/4}\]

Answer 16

and then apply that outer exponent of 1/4 to everything inside

\[\Large \left(16x^{8}y^{17}\right)^{1/4} = 16^{1/4}*\left(x^{8}\right)^{1/4}*\left(y^{17}\right)^{1/4}\]

Answer 17

what's next?

Answer 18

im completely lost... so 2^4=16? and to simplify x^8 it would be (x^2)^4? @jim_thompson5910

Answer 19

Do you see how I got up to

\[\Large 16^{1/4}*\left(x^{8}\right)^{1/4}*\left(y^{17}\right)^{1/4}\]

??

Answer 20

i see it because the radical expression had 4.... right?
so 16/4=2 and checking 2^4 it equals 16. i just don't get how to simplify the variables

Answer 21

yep so because

\[\Large 2^4 = 16\]

this means

\[\Large \sqrt[4]{16} = \sqrt[4]{2^4}\]

\[\Large \sqrt[4]{16} = \left(2^4\right)^{1/4}\]

\[\Large \sqrt[4]{16} = 2^{4*(1/4)}\]

\[\Large \sqrt[4]{16} = 2^{1}\]

\[\Large \sqrt[4]{16} = 2\]

Answer 22

For the x term, you do the same thing

\[\Large \left(x^{8}\right)^{1/4} = x^{8*(1/4)}\]

\[\Large \left(x^{8}\right)^{1/4} = x^{2}\]

Answer 23

What do you when you simplify the y term?

Answer 24

for y^17... would you put it in radical form?

Answer 25

how would you simplify \[\Large \left(y^{17}\right)^{1/4}\]

Answer 26

y^17/4?

Answer 27

what is 17/4 equal to?

Answer 28

4.25?

Answer 29

fill in these blanks

17/4 = _____ remainder _____

Answer 30

4 remainder of 25?

Answer 31

the first part is right, but having a remainder of 25 is not

Answer 32

4 goes into 17 four whole times

since 4*4 = 16

Answer 33

the remainder is the amount left over

17 - 16 = 1

Answer 34

17/4 = 4 remainder 1

Answer 35

ohhh

Answer 36

why do we care about this? well because we can use that quotient/remainder to convert 17/4 to a mixed number

\[\Large \frac{17}{4} = 4\frac{1}{4}\]

Answer 37

so...

\[\Large \left(y^{17}\right)^{1/4} = y^{17/4}\]

\[\Large \left(y^{17}\right)^{1/4} = y^{4 \frac{1}{4}}\]

\[\Large \left(y^{17}\right)^{1/4} = y^{4 + \frac{1}{4}}\]

\[\Large \left(y^{17}\right)^{1/4} = y^{4}*y^{\frac{1}{4}}\]

\[\Large \left(y^{17}\right)^{1/4} = y^{4}*\sqrt[4]{y^1}\]

\[\Large \left(y^{17}\right)^{1/4} = y^{4}*\sqrt[4]{y}\]

Answer 38

In other words, I'm saying

\[\Large \sqrt[4]{y^{17}} = y^{4}*\sqrt[4]{y}\]

Answer 39

so would it be...\[2x ^{2}y ^{4}\sqrt[4]{y}\]?

Answer 40

that's one form of the final answer

however, they want all radicals to be in exponential form

so

\[\Large 2x^2y^4\sqrt[4]{y} = 2x^2y^4y^{\frac{1}{4}}\]

Answer 41

ohh okay another question.. how would the text format be when i enter it in? would it just be 2x^2y^4y^1/4?

Answer 42

enclose the exponent in parenthesis to make sure the computer knows that 1/4, and not just 1, is the exponent.

Answer 43

so for sure that the system wants it in exponential form?

Answer 44

hmm now that I think about it, it's probably just more efficient and time-saving to just write 2x^2y^(17/4)

Answer 45

it says so on the problem posted

Answer 46

it said that it was wrong:c

Answer 47

for \[\Large \sqrt[n]{b}\] enter (b)^(1/n)

Answer 48

what did you type in?

Answer 49

did you try 2x^2y^(17/4)

Answer 50

I have a feeling that's what it wants

Answer 51

yes i tried that. :o

Answer 52

ok why not try 2x^2y^4y^(1/4)

Answer 53

and just put the exponents in parenthesis?

Answer 54

yeah, esp the 1/4

this is because y^1/4 means (y^1)/4 to the computer

Answer 55

using PEMDAS, exponentiation comes first, so that explains why the computer thinks y^1/4 means (y^1)/4

Answer 56

im still having trouble entering it in...

Answer 57

the computer is just being a pain at this point

hmm what else to try

Answer 58

hahaha its alright! i finally got it :) i put it in
"2x^2y^4(y)^(1/4)

Answer 59

oh forgot the parenthesis around the y, i see now

Answer 60

thank you so much for your help!!

Answer 61

np