Question

Simplify completely 18 s t to the fourth power over 52 s cubed t times 16 s cubed over 9 s squared t???
help please :x

Answer 1

Can you write it numerical?

Answer 2

18st^4 16s^3
------- *--------
52s^3t 9s^2t

Answer 3

\[\large \large \frac{ 18st^4 }{ 52s^3t } \times \frac{ 16s^3 }{ 9s^2t }\] ^It looks like this?

Answer 4

yes ^.^

Answer 5

Alright. So what do you think you want to do first?

Answer 6

simplify...i have no idea:/

Answer 7

Do you know how to cross multiply?

Answer 8

yes

Answer 9

Alright, so what is 62s^3t * 16s^3 ?

Answer 10

well i got 992s^3t...doubt thats right lol

Answer 11

Let take it step-by-step. :)
What is 62 * 16? It is 992.
But what is s^3 * s^3?
Do you remember the Laws Of Exponents?

Answer 12

its suppose to be 52 not 62 >.< btw ..and no

Answer 13

(52*16=832)

Answer 14

Opps my bad.

Answer 15

Alright, the Laws Of Exponents say
"To multiply powers of the same base, add the exponents"
In this case, 1 is the base. Do you understand?
Btw, you should remember this, it is very important!

So what is s^3 * s^3?

Answer 16

its 1?

Answer 17

The base is 1.
So s^3 * s^3 can be written as 1s^3 * 1s^3.

So what would it give us? It's not 1.

Answer 18

2s^3?

Answer 19

Well. According to the Laws Of Exponents, you add the exponents.
So we have 3 and 3.
What is 3+3?

Answer 20

6

Answer 21

Alright. So s^3 * s^3 = s^6.
Make sense so far?

Answer 22

ohhhh yes makes sense lol

Answer 23

So far, we have 832s^6. But what about the "t"?
Well, we just leave it as t because you can't multiply t by anything.
So we should get 832s^6t.

Now what's 18st^4 * 9s^2t ?

Answer 24

18 * 9 does equal to 162.
But I don't understand the ^10 part.

So we have to do st^4 * s^2t.

What does s * s^2 give you?

Answer 25

1^6

Answer 26

Not quite. The base is 1.
So another way of writing it is 1s * 1s^2,
They both have the same base.
So according to the Laws of Exponents, we add the exponents.
So what do we get?

Answer 27

wouldnt you add 2 and 4

Answer 28

What do you mean? I'm talking about "s * s^2"

Answer 29

2^2

Answer 30

Here's 2 big tips:
When you're multiplying a coefficient by a coefficient (A number times a variable. Ex: 1x, 10y, 205a) there should always be a variable. So what happened to the variable s? o_O

And 2nd step, when you see a number/variable without an exponent, ex:
s, 10, 100, 1000, a, d... there's always an invisible 1.
So s can be s^1. 10 can be 10^1. and so on.

So s is s^1.
s^1 * s^2 is?

Answer 31

1s^2

Answer 32

What's 1 + 2?

Answer 33

3

Answer 34

So s^1 * s^2 = s^3. :)

Now we are left with t^4 and t. What does that give us?

Answer 35

1^4

Answer 36

Remember what I said before?
What exponent does t has?

Answer 37

2^4

Answer 38

Listen to what I said. :)
What exponent does t has?
Does it have ^1, ^2, ^1000, ^-1?

Answer 39

ehhhhhhhh idk i give up lol

Answer 40

No no! Don't give up! Just read what I said before. :) The tip I gave you. It can certainly help you. :)

Answer 41

invisible 1 lol

Answer 42

Alright!!! Good job.
So t is t^1. What is
t^1 * t^4?

Answer 43

t^5

Answer 44

Good job!!! So now our if you combine them, it looks like:
162s^3t^5 = 832s^6t

Answer 45

thats it?...

Answer 46

\[\large \large 162s^3t^5 = 832s^6t\] (Just to make it look easier to see)
Are we suppose to find a variable, or just simplify in general?

Answer 47

simplify completely

Answer 48

Hmm. I thought we were suppose to find the variable. But if it's just simplify completely, I guess this is simplify completely. Let me ask @ganeshie8

Answer 49

okay :)

Answer 50

Hmm. I think it means simplify as in simplify the fraction. o_o
So let's do that, it's much easier. Alright?

Answer 51

answer choices: a)8t^2/13s
b)8t/13s^2
c)4t^2/13s
d)4t/39s^2

Answer 52

Lolol. You should've told me that. :|
So we have to simplify the fraction first.
Okay?

Answer 53

What does 18/52 simplify to?

Answer 54

9/26

Answer 55

Now remember what he said before, right?
When you multiply 2 variable with an exponent, you add the exponent, right?
Well, for division, instead of adding, you subtract the exponent.

Answer 56

s^4/s^3 *

Answer 57

s^1

Answer 58

Opps. My bad. Yes s^4/s^3 does give you s.
I meant to say, what is s/s^3?

Answer 59

-2?

Answer 60

Wow! Yes! Really good.

Answer 61

What is t^4/t ?

Answer 62

t^3

Answer 63

Alright. So: \[\large \large \frac{ 18st^4 }{ 52s^3t } = \frac{ 9s^-2t^3 }{ 26 }\] What about the other fraction.
What does 16/9 simplify to?

Answer 64

I just realize, I've been helping you for an hour. :O A lot of time-consuming. :)

Answer 65

thats why i hate math it a waste of time :) and doesnt it stay the same?

Answer 66

Which one? 16/9?

Answer 67

yeah

Answer 68

In improper fraction form, yes. But in mixed number form, what would it be?

Answer 69

i dont know :x

Answer 70

Alright. Let skip that. What does s^3/s^2?

Answer 71

s^1

Answer 72

Correct! Or just s. So:

\[\large \large \frac{ 16s^3 }{ 9s^2t } = \frac{ 16s }{ 9t }\]

Answer 73

Make sense so far?

Answer 74

yes :)

Answer 75

Now: \[\large \large \frac{ 9s^-2t^3 }{ 26 } * \frac{ 16s }{ 9t }\]

Answer 76

Wait a few min. I have to do something.

Answer 77

okay :)

Answer 78

I have to go. But the answer is 8t^2/13s

Answer 79

thank you so much for your help :)

Answer 80

This is correct!
The answer is A) 8t^2/13s