Question

Please help URGENT!!!!

Answer 1

@zepdrix @mathmale

Answer 2

\[\large\rm \frac{\color{orangered}{(a^{-1}b^3)^{3/4}}}{(ab)^{-3/4}}\]Deal with the numerator first.
You'll need to apply this 3/4 exponent to BOTH the a and b separately.

Answer 3

\[\large\rm (a^{-1})^{3/4}=a^?\]

Answer 4

I don't understand how this works can you help me through it

Answer 5

When you have an exponent being applied to multiple things,
you have to give the exponent to each of them.
Example: \(\large\rm (xy)^3=(x)^3(y)^3\)
I had to give the 3 to both the x and the y.

So here is what we're dealing with:
\(\large\rm (a^{-1}b^3)^{3/4}=(a^{-1})^{3/4}(b^3)^{3/4}\)
I gave the 3/4 exponent to each thing in the brackets.

Answer 6

Okay so would it be A^-3/4?

Answer 7

Yes, good.
Your exponent rule tells you to `multiply` when you have a power and a power like that.

Answer 8

How bout the b?
What is 3 * 3/4?

Answer 9

Wouldnt that give me a decimal?

Answer 10

Well, we'd like to leave it in fraction form :\
Forgot how to multiply a whole number and fraction?
Recall that a whole quantity can be written over 1.
So 3 is 3/1.
That will make it easier to multiply them together.

Answer 11

A^6/4? or A^4/6?

Answer 12

\[\large\rm 3\cdot\frac{3}{4}\quad=\frac{3}{1}\cdot\frac{3}{4}\quad=\frac{3\cdot3}{1\cdot4}\]

Answer 13

No 6 :)

Answer 14

my bad it would be nine lol XD

Answer 15

Brain fart haha

Answer 16

\[\large\rm \frac{\color{orangered}{(a^{-1}b^3)^{3/4}}}{(ab)^{-3/4}}\quad=\frac{\color{orangered}{a^{-3/4}b^{9/4}}}{(ab)^{-3/4}}\]Ok good, that takes care of the numerator.

Answer 17

then it would be (A^-3/4 B^-3/4) right?

Answer 18

Mmm k good.

Answer 19

Anything else I should do?

Answer 20

\[\large\rm \frac{a^{-3/4}b^{9/4}}{a^{-3/4}b^{-3/4}}\]

Answer 21

It tells me to write it without negatives so just take them out?

Answer 22

Nah, let's not do anything about the negatives just yet.
Let's try to divide first, if we're able to.

Answer 23

Notice the a's have the `exact same exponent`.
What does that tell you?
Anything? :)

Answer 24

they divide evenly?

Answer 25

Good good good, they divide evenly,
or sometimes we call that "cancelling out"

Answer 26

So we can just get rid of the a's.

Answer 27

\[\large\rm \frac{b^{9/4}}{b^{-3/4}}\]

Answer 28

Now apply your exponent division rule:
\(\large\rm \dfrac{x^c}{x^d}=x^{c-d}\)

Answer 29

okay so b^12?

Answer 30

So your exponent is going to be 9/4 - (-3/4) right?
Hmm I don't think that turns into a 12 0_o

Answer 31

So a^12/8?

Answer 32

or b i mean

Answer 33

Ahh you gotta brush up on some of those basic math skills bruh :)
When we add/subtract fractions, we only change the numerator

If you have 9 of these things called "fourths"
and you add 3 more of these "fourths"

you get 12 of these "fourths", ya?
They don't magically become some other type of thing.

Answer 34

Okay

Answer 35

Im bad at math lol sorry

Answer 36

b^{12/4}

Ok I think we can simplify this a tiny bit further :)

Answer 37

b^3/1?

Answer 38

Good good good.
And a 1 is pretty insignificant, so we'll write it like this: b^3

Answer 39

yay team \c:/ we did it!

Answer 40

Okay

Answer 41

I don't know how to put it all together now

Answer 42

how would I write

Answer 43

How would you write your final answer?
Or you mean you have to explain the steps?

Answer 44

Write the final answer

Answer 45

The final answer simplified aaaaall the way down to b^3.

Answer 46

really well darn lol

Answer 47

The a's divided evenly, so poof, they vanished.
And we applied exponent rule to turn the multiple b's into a single b

Answer 48

Thanks your the best, I wish I learned this all when i was being taught it ;-; but I didn't thought I was coollol

Answer 49

XD

Answer 50

Time to rationalize the denominator