Question

Need Help with liberal Arts math! Can anyone help?

Answer 1

ill try to help u

Answer 2

ok so what is the question?

Answer 3

Alright let me type this down...sorry.

Answer 4

Simplify the expression and rewrite in rational exponent form.

Answer 5

Im simplifying it slowly...so far i got x^3/2*24y*y^3/4 over 3x^1/2* 4x^2/3

Answer 6

@xapproachesinfinity I honestly dont know what to do next.

Answer 7

sorry i was away :(

Answer 8

okay let us see what do we have here

Answer 9

ok so far good start

Answer 10

first simplify the bottom more

Answer 11

you have x^something times x^ another thing
see you add up the power following this rule \[a^na^m=a^{n+m}\]

Answer 12

Can i say what i got for my answer?
I got,
X^5/3 Y^3/4 over 2?

Answer 13

seems wrong!!

Answer 14

let's how it is done!

Answer 15

Alright, let me retry this sorry, its hard im juggling a lot of work...

Answer 16

\[\frac{24x^{\frac{3}{2}}yy^{\frac{3}{4}}}{12x^{\frac{1}{2}}x^{\frac{2}{3}}}=\frac{2x^{3/2}y^{7/4}}{x^{7/6}}\]

Answer 17

i used the property described above

Answer 18

when the base is the same you add up the exponents

Answer 19

then you need one more property to simply more
x^n/x^m=x^n-m

Answer 20

Okay so for once of my answers could it be 2x^1/3y^7/4?

Answer 21

Also I hope you dont mind helping me with a couple more...im really confused.

Answer 22

actually it is the answer

Answer 23

You're joking...
Wow!! Your explanation helped a ton...can you help me with some more? Maybe like one or two more? :/

Answer 24

Thank you so much, your helping my brain out :)

Answer 25

sure :)

Answer 26

same thing for this one.

Answer 27

\[7c \sqrt[3]{d^5}\]

Answer 28

That was my answer...

Answer 29

excellent!!

Answer 30

any others?

Answer 31

REALLY?! I just scribbled on that one. literally took me a week. yes about two more.

Answer 32

ok

Answer 33

once you get this it takes no time

Answer 34

Assume a and b are nonzero rational numbers and c is an irrational number. for each following expression determine whether the result is rational, irrational or both.

Answer 35

Let me put the other part down

Answer 36

ok

Answer 37

Part A: a(b+c)
Part B: \[(a \sqrt{7})^2\]
Part C: ab+ab^2

Answer 38

Now looking at part A i believe its rational

Answer 39

let's see
we know a and b are rational and c irrational
we start with b+c
rational added to irrational the result will be irrational

Answer 40

and a rational multiplied by an irrational gives us an irrational?

Answer 41

then if you multiply irrational with rational you will still get irrational
take an example
pi
add 3
3+pi
if you multiply you get 2(3+pi)=6+2pi which is still irrational

Answer 42

yes

Answer 43

Part b is easy

Answer 44

Alright now for part...B..im going to look this one over quick

Answer 45

ok i will let you that one let's how you argue it rationality

Answer 46

Looking through my notes it looks like it would be rational but then again, i could be wrong because of the square root of 7...that leaves a decimal that doesnt repeat a pattern, let me check again..

Answer 47

on it can be proven that if a is rational (sqrta)^2 is rational too
obviously a=(sqrta)^2

Answer 48

Yup it doesnt have a pattern to it and it doesnt end.

Answer 49

so does that mean it would be rational?

Answer 50

not that(sqrt7)^2 is a perfect square

Answer 51

now thinking about it, could it actually be both?

Answer 52

don;t be confused sqrt7 by itself is irrational
but with square the square root cancels

Answer 53

Oh so it is rational because of the ^2

Answer 54

no it cannot be either rational or irrational
there is no such thing as both

Answer 55

exactly!

Answer 56

so (a sqrt7)^2=a^2(sqrt7)^2
since both a^2 and (sqrt7)^2 are rational the entire # is rational

Answer 57

i i guess last is most easier
just product and addition of rational numbers

Answer 58

Thank you again! Your literally a life saver, Alright Part C...

Answer 59

it can be easily seen what it is

Answer 60

This looks like its rational. :)

Answer 61

yes it is

Answer 62

just additioon and product of numbers that are rational

Answer 63

no problem, glad i was of help

Answer 64

Alright, Just one more but im pretty sure i can handle it. I dont know if you want to take a look.

Answer 65

make it quick i need to go :)

Answer 66

Okay find the value of ____ and place it in simplest form.

Answer 67

Im pretty sure this one is irrational as well.

Answer 68

but the question is not asking for that?

Answer 69

thats the second part of that

Answer 70

sorry i forgot to add that.

Answer 71

ok that is most simple form
and it is rational
0.22 recurring is rational but radical 112 is not rational

Answer 72

that's allright?

Answer 73

Alright, so that would still mean its irrational correct?

Answer 74

yes

Answer 75

Woo!! Thank you so much! I owe you one :)

Answer 76

my pleasure! i happy if y learned enough from me:)

Answer 77

I did thank you thank you thank you :)