Question

I have this math equation that I need help with, if anyone can help me.
(25x^3)^2/3 the 2/3 is in a fraction form
-----------
(125xy^2)^1/3 the 1/3 is in a fraction form too..

Answer 1

So in total does it look like \[\frac{(25x^3)^{\frac{2}{3}}}{(125xy^2)^{\frac{1}{3}}}\]?

Answer 2

Or are the two parts equal to each other?

Answer 3

that looks exactly..

Answer 4

the same

Answer 5

Alright. So is the objective to simplify the fraction?

Answer 6

yeah, i don't know where to start...

Answer 7

my internet doesn't want me to help u....I'm trying to upload the pic but nothing :(:(:(

Answer 8

\[(\sqrt{25})^{3}(x ^{3})^{2/3}\]
Numerator will be 125x^2

Answer 9

It's definitely a tough one. Let me see if I can make it look a bit nicer \[\frac{(25x^3)^{\frac{2}{3}}}{(125xy^2)^{\frac{1}{3}}}=\left[\frac{(25x^3)^2}{125xy^2}\right]^{\frac{1}{3}}\]

Answer 10

i expressed 25 as 5^2 and 125 as 5^3 and then subtracted the exponents

Answer 11

\[(\sqrt[3]{125})*(\sqrt[3]{x})*(\sqrt[3]{y ^{2}})\]

Answer 12

I don't think you can subtract the exponents when they're inside brackets taken to different powers. You'd have to apply the square to the numerator before you could do that.

Answer 13

i have expressed them the same with base=5 and
if a^x/a^y=a^(x-y) isn't it?

Answer 14

Yes, but that is not quite the case here. You have \[\frac{(a^x)^{\frac{2}{3}}}{(a^y)^{\frac{1}{3}}}\] You need to bring that 2 inside, so it's \[\frac{(a^{2x})^{\frac{1}{3}}}{(a^y)^{\frac{1}{3}}}\]

Answer 15

yea :):)
I'm not gonna write anymore :) u keep going with ur solution cause it is right as well :):):):)
sorry :)

Answer 16

Anyway, if you're still around monika, how did you get on with that?

Answer 17

I have no idea, what to do...

Answer 18

Dalvoron, can u show me again

Answer 19

Alright, well let's start with the last thing I posted \[\left[\frac{(25x^3)^2}{125xy^2}\right]^{\frac{1}{3}}\] The first thing I want you to do is apply that power of 2. Just look at the \((25x^3)^2\) for now, and try to apply that square.

Answer 20

Use the rule \((a b)^2 = (a^2b^2)\)

Answer 21

ok

Answer 22

What do you get when you do that?

Answer 23

ok, hang on.. still working on it..

Answer 24

do i work with 25x^3 becomes as what

Answer 25

Yep

Answer 26

but what happens with ^2

Answer 27

You have to apply it to the 25, and the \(x^3\)

Answer 28

ok, so its (25^2) (x^3)^2

Answer 29

Yep, and what does that equal?

Answer 30

625 but i don't know how to solve (x^3)^2

Answer 31

The 625 is right. Use the rule that \(x^a)^b = x^{(a)(b)}\)

Answer 32

ok, so its.. x^6

Answer 33

right

Answer 34

Alright, so now we have \[\left[\frac{(25x^3)^2}{125xy^2}\right]^{\frac{1}{3}}=\left[\frac{625x^6}{125xy^2}\right]^\frac{1}{3}\]

Answer 35

Since everything is inside one pair of square brackets, the next step is to ignore them for the moment, and focus on the fraction \[\frac{625x^6}{125xy^2}\] How would you simplify that?

Answer 36

do i divide the 625 by 125

Answer 37

Yep, that's one of the two things you do at this stage.

Answer 38

What does the fraction look like after you do that division?

Answer 39

i got 5x^6
-----
xy^2

Answer 40

That's right! What else could you do to simplify the fraction?

Answer 41

no clue

Answer 42

Let's say you had just the xs there, so your fraction was \[\frac{x^6}{x}\] Could you simplify that?

Answer 43

can it be 2, 6 divided by 2 and the answer is 3

Answer 44

Not that, no. I'll try to write it differently, maybe it will help. \[\frac{x^6}{x} = \frac{x \times x \times x \times x \times x \times x}{x}\]

Answer 45

it becomes x^5 cause one set of the x's cancels out..

Answer 46

Exactly

So now your fraction is \[\left[\frac{5x^5}{y^2}\right]^\frac{1}{3}\]

Answer 47

As far as I can tell, it doesn't get any simpler than that.

Answer 48

this equation looks simple for you but not for me... so, from here what else do I do...

Answer 49

What I mean is that I think that is the end of the question.

Answer 50

lol.. oh, i knew that..

Answer 51

Is this multiple choice?

Answer 52

what..

Answer 53

The answer Dal helped you with is good. But sometimes, with multiple choice answers, it won't be there... there are other ways to write this expression. For example
\[(5 x^{5}y^{-2})^{\frac{1}{3}}\]