Question

how do you evaluate like like variables with exponents?
such as, 3^-4 * 3^4

Answer 1

No difference. Remember
\[\Large a^ma^n = a^{m+n}\]
It always applies, even with negative exponents.

Answer 2

oh ok, and if i were to simplify the product i would just find the reciprocal, right?

Answer 3

First, what's your product in its 'raw' form (ie, just add their exponents)

Answer 4

i'm trying to figure it out. the problem is to evaluate 3^-3 * 3^4 * 3 * 3^-5

Answer 5

i know how to add the exponents but how do i incorporate that into multiplying the bases

Answer 6

You don't multiply bases :)
If they're the same base, you just copy the base. Let me illustrate:
\[\Large \color{red}{a^2}\cdot\color{blue}{ a^4}\\\Large =\color{red}{a\cdot a}\cdot \color{blue}{a\cdot a\cdot a\cdot a}\\\Large = a^6\\\Large = a^{\color{red}2+\color{blue}4}\]

Answer 7

i know that but these bases are numbers. does that principle still count the same for variables and numbers?

Answer 8

Yup :)
Variables are just placeholders for numbers :D

Answer 9

the answers dont have a 3 in them D:

Answer 10

omg algebra >.<

Answer 11

Okay, first tell me the answer in its raw form. Just the 3 and its exponent... what is it?

Answer 12

3^-3 ?

Answer 13

<ahem>
-3 , 4 , -5 ???

Answer 14

Could you add these up again? :3

Answer 15

is the answer

Answer 16

;-;

Answer 17

I don't know. Check it. What is the answer in its raw form?

Answer 18

-81 ?..

Answer 19

:(

Answer 20

ugh

Answer 21

-81?
I don't even...

Answer 22

i feel really stupid right about now

Answer 23

Come on, you were close. I told you: Copy the base, and its exponent would be the sum of all the exponents in the factors.

Answer 24

-3

Answer 25

YES. right?..

Answer 26

No.

Answer 27

shame

Answer 28

\[\Large 3^{-3}\cdot 3^4\cdot 3^{-5}\]

Answer 29

Step by step... copy the base... what's the base?

Answer 30

waitwaitwaitwaitwait

Answer 31

waiting

Answer 32

3^-3 * 3^4 * 3 * 3^-5

Answer 33

that was the problem

Answer 34

Oh. Well, in that case, all correct :P
Except...

Answer 35

Sorry for that mix-up :3

Answer 36

what about the lone three? since it has no exponent doesn't that automatically give it an exponent of 1?

Answer 37

Yes, it does.

Answer 38

so i was right ._.

Answer 39

\[\Large 3^{-3}\]
Then, and you're correct up to this point.

Answer 40

oh my god

Answer 41

im so done

Answer 42

Something wrong?

Answer 43

Form the looks of it, that's not your final answer yet.

Answer 44

XD thanks for youe help. i know more on how to work these kinds of problems out

Answer 45

wait what

Answer 46

you're kidding

Answer 47

Well, is \(\Large 3^{-3}\) one of your choices?

Answer 48

no i was thinking it was 1/81

Answer 49

It isn't.

Answer 50

okay well my other answer is 1/27

Answer 51

You can't have two different answers.
I want you to be sure.
Next rule on exponents.
\[\Large a^{-n}\]

Answer 52

When you have a negative exponent, it may be brought down to the denominator AND THEN replaced with a positive exponent.
\[\Large a^{-n} = \frac1{a^n}\]

Answer 53

What does that bode for
\[\Large 3^{-3}=\color{red}?\]

Answer 54

yes. it was -27 then i turned it to 1/27. okay this answer is right. i know it is

Answer 55

It's not -27 :/
-27 is not the same as 1/27.

Better write it as \(\Large 27^{-1}=\frac1{27}\)

Answer 56

k

Answer 57

So much for that.

Answer 58

he answers are
a.-27
b.1/27
c.-81
d.1/81

Answer 59

it's b

Answer 60

Show me that you understand how to do this...
What would be the fraction form of \[\Large 5^{-2}=\color{red}?\]

Answer 61

-10?...

Answer 62

Nope. I told you...
\[\Large a^{-n}= \frac1{a^n}\]

Answer 63

ugh i feel like a complete idiot.

Answer 64

i'm trying to understand all of this but it's difficult

Answer 65

Okay. Let's start at square one again...
\[\Large a^{-n}=\]

Answer 66

1/a^n

Answer 67

Okay... in that case, what's \[\Large 5^{-2}=\color{red}?\]

Answer 68

i dont know...

Answer 69

That's why you should not jump straight to the answer and ignore the process -.-
Now...
\[\Large a^{-n }=\]

Answer 70

When you have a negative exponent, you bring the base into the denominator...
\[\Large a^{-n}= \color{red}{\frac1{a^?}}\]

Answer 71

look dude i really appreciate your help but i clearly dont have the mental capacity to understand this stuff. i'm just going to go ask a physical person for help. that usually does better for me. thanks anyways mate.

Answer 72

And its new exponent would be its previous exponent, multiplied by -1.
\[\Large a^{-n}=\frac1{a^{-n\cdot-1}}=\frac1{a^n}\]