Question

simplify the expression (logs) (alg 2) (will medal those who help me understand)

Answer 1

Hi, go ahead

Answer 2

What's the problem?

Answer 3

\[\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }\]

Answer 4

Would you agree that

(a/b) * (c/d) would equal ac/bd?

Answer 5

Idk what that means

Answer 6

a b c and d are letters that represent numbers called variables because we don't what numbers they are

Answer 7

\[a^x \times a^y = a^{x + y}\]

\[\frac{ a^x }{ a^y } = a^{x - y}\]

Answer 8

If I multiply two fractions all I need to do to get the product is multiply across..

1/2 times 3/4 is an example, what would that be?

Answer 9

3/8

Answer 10

Right so first step, multiply accross..

Answer 11

20e^-20?

Answer 12

rishavraj left a formula that will be useful when multiplying terms with exponents

Answer 13

what? 0.0

Answer 14

"\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }\[\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }\] is an expression, not an equation, so NO cross mult applies here. Neither can you "solve" for anything. You can only reduce the given expression.

Answer 15

In your shoes I would combine \[e ^{-4 }~and~e^5 \] thru multiplication; result is just e.

Answer 16

So, reduce the given expression as much as possible.

Answer 17

what do you do with the 10 and the 2?

Answer 18

In the expression \[\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }\] you have 10 in the numerator and 5 in the denom. Reduce this fraction.

Answer 19

Can't do anythign with the 2 in the numerator and the 3 in the den. other than keep them as is.

Answer 20

that still makes no sense

Answer 21

2 and 10 you can multiply across to get 20
just as you can with the numberical portion of the denominator

but when you e^-4 and you are multiplying by e^5 instead of multiply the exponents we add them

say it was 2^5 times 2^2 that will not equal 2^10
that will equal 2^7

Answer 22

Re: "that still makes no sense:" Rather than say that, would you please try to phrase questions whose answers might make things less confusing to you. "that still makes no sense" leaves the problem dumped into the other person's lap.

Answer 23

So multiply through numerically and add through left to right with the terms of e

Answer 24

10/5 = 2, right? so the 10 and 5 disappear and are replaced by a 2 in the numerator.
2/3 stays as it is (this fraction can't be reduced).

Answer 25

you said we aren't cross multiplying

Answer 26

so, where are we now? What do y ou need to know to complete the simplification of the expression \[\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }~??\]

Answer 27

Know you are multiplying through right?

a b / cd = a / c times b / d

Answer 28

Cross multiplication? first, I ask you how cross mult. might help and why you think it applies here.

Cross mult. has its place when you are working with equations involving fractions.
You don't have an equation here. You have an expression which involves fractions.

Answer 29

therefore, no cross multiplication. Instead, reduce ()which involves division, not mult.).

Answer 30

\[\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }\]

Answer 31

In this situation

we have a over b times c /d in that each term is unique so you see the process we must take?

Answer 32

1. Divide that 5 into that 10.
2. Combine e^(-4) and e^2 into ONE exponential, to appear in the numerator.
3. Combine e^5 and e^(-3) into ONE exponenetial, to appear in the numerator.
4. Combine the 2 expressions in the numerator that involve exponentiation.

Answer 33

2e^7 is what I got from 10e^5/5e^2

Answer 34

Do you agree we'd have this if we multiply through?
\[(2e ^{-4})(10e ^{5}) / (5e ^{2})(3e ^{-3})\]

Answer 35

Multiply across left to right

Answer 36

Can't reduce the 2/3.

Start your "answer" by typing \[\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }\rightarrow \frac{ 2 }{ 3 }*\frac{ 2e^1 }{ e ^{-1} }\]

Answer 37

As daniel suggested, I am multiplying from left to right. \[e ^{-4}e^5=e^1=e\]

Answer 38

So we'll have 20e^( ) / 15e^ ( )

Can you fill in the blank knowing

a^x times a^y = a^ x + y for any number value a

Answer 39

I don't know where you're getting e^-1

Answer 40

e^2 times e ^-3

Answer 41

then where are you getting 10/5

Answer 42

On the bottom we have 5e^2 (3e^-3)

We multiply the numbers and add the exponents

Answer 43

Please make a table of Rules of Exponentiation:\[a^b a^c = a ^{b+c}\]...and so on.

Answer 44

\[a^b a^c=a ^{b+c}\]

Answer 45

...and so on. You'll need to know these rules.

Answer 46

"Where did y ou get the 10 and 5?" Please refer back to the original problem statement, the expression \[\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }\]

Answer 47

The 10 is in the numerator and the 5 in the denom.

Answer 48

right, so that makes 2

Answer 49

Yes, it does. 2/3 can't be reduced, so leave that as is. Mult. 2 and (2/3), you get (4/3). OK with that?

Answer 50

Then you'll need to apply rules of exponentiation to simplify the rest of this expression, which consists of exponential quantities.

Answer 51

where are you getting the other 2 from?

Answer 52

(4/3) is the same as (20/15) which is what you get when you multiply left to right

Answer 53

Please refer to the original expression:\[\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }\]

Answer 54

\[\frac{ 2e ^{-4}}{ 5e ^{2} }*\frac{ 10e ^{5} }{ 3e ^{-3} }\]

Answer 55

That "2" comes from dividing 10 by 5. We've discussed that several times.
The (2/3) comes from the 2 in the numerator and the 3 in the denom.

Answer 56

So, again, you have (4/3) times a fraction involving powers of e. Combine all those powers of e into one exponential expression.

Answer 57

okay so I got 4e/3e^-1?

Answer 58

Yes. But that could be simplified to look much better:
\[\frac{ 4 }{ 3 }\frac{ e }{ e ^{-1} }=?\]

Answer 59

4/3 *1/e?

Answer 60

simplify that. this is the last step. Please, if you've written down those rules of exponents as I've suggested, use the appropriate one to simplify \[\frac{ e }{ e ^{-1} }.\]

Answer 61

Your most result result is almost, but not quite, right. Reduce:\[\frac{ e }{ e ^{-1} }.\]

Answer 62

what rules are you talking about?

Answer 63

Study_Buddy: I've mentioned rules of exponentiation at least twice in our previous exchanges, recommending that you look them up and copy them down for later reference. I'm a bit concerned because you apparently haven't seen or understood what I'm asking you do do, which has apparently led to your asking questions that have already been answered.

I gave you the rule\[e^a e^b=e ^{a+b}\]

Answer 64

Several others follow:\[e^a/e^b=e ^{a-b}\]

Answer 65

\[(e^a)^b=e ^{ab}\]

Answer 66

Please, do an internet search, or look in the index of your algebra textbook, for "exponents, rules of" ... and copy down these rules, study them and review them from time to time.

Answer 67

I don't understand the rules. I don't understand what they represent. I don't understand when they use them.

Answer 68

think: 1) multiplication of exponential functions
2) division of exponential functions
3) powers of exponential functions

do you have a textbook available? If so, would you please look up "exponents, rules of?"
Otherwise do the same search on the Internet.

If you want my help in deciding which rule to apply in a given case, find some homework problems involving exponential functions and share them with me. Before doing so, compare the problems with the several rules of exponents that I gave you and make a preliminary decision regarding which one to use for which case.

It is essential that you learn to do this (practice selecting the appropriate rule to apply to a given homework problem).

Answer 69

Is there any way in which you could find a live tutor with whom to interact when you feel stuck like this? I have the feeling you'd understand me a bit better were we meeting face to face, not through the Internet.

Answer 70

I will be back on OpenStudy tomorrow morning, in case you decide to share any more questions with me. I need to get off the 'Net now.

Answer 71

yeah, I'll see someone tomorrow. Thank you for being so persistent with me, I've never seen these rules in my life.