# Exponents

• Sep 26th 2007, 03:17 PM
JonathanEyoon
Exponents
We've been on exponents for a little while now in class and I keep getting confused :p. Bear with me please.

I'm to simplify

(3x(sqrt(x^3))^2

From here I

(3^2)(x^2)(x^3)

9x^5

Next one is

x^e(x^e)^2

(x^e)(x^2e)

x^(2e + e)

Please let me know if I did those correctly =)
• Sep 26th 2007, 03:43 PM
mahurshi
Quote:

Originally Posted by JonathanEyoon
We've been on exponents for a little while now in class and I keep getting confused :p. Bear with me please.

I'm to simplify

(3x(sqrt(x^3))^2

From here I

(3^2)(x^2)(x^3)

9x^5

Next one is

x^e(x^e)^2

(x^e)(x^2e)

x^(2e + e)

Please let me know if I did those correctly =)

both are correct. why don't you write x^(3e) for the second one ;)
• Sep 26th 2007, 04:03 PM
JonathanEyoon
Quote:

Originally Posted by mahurshi
both are correct. why don't you write x^(3e) for the second one ;)

You know I thought about doing that but I thought it was wrong :confused:
• Sep 26th 2007, 04:11 PM
JonathanEyoon
For the next two, it's not part of our graded homework assignment but I'd still like to know how to do them if you guys don't mind :p.

((y^-2)(e^y))^2

(y^-4)(e^2y)

e^(2y) / y^4 <------------- Did I do that correctly ?

Next one is:

4x^(3pi + 1) / x^2

4^(3pi + 1) / x

From here I multipled 3pi + 1 = 10.4247796.

So would the final answer be 10.4247796 / x ?
• Sep 26th 2007, 04:13 PM
topsquark
Quote:

Originally Posted by JonathanEyoon
For the next two, it's not part of our graded homework assignment but I'd still like to know how to do them if you guys don't mind :p.

((y^-2)(e^y))^2

(y^-4)(e^2y)

e^(2y) / y^4 <------------- Did I do that correctly ?

Next one is:

4x^(3pi + 1) / x^2

4^(3pi + 1) / x

From here I multipled 3pi + 1 = 10.4247796.

So would the final answer be 10.4247796 / x ?

The first one is correct, the second one has a problem.

$\frac{4x^{3 \pi + 1}}{x} = 4x^{3 \pi + 1} \cdot x^{-1} = 4x^{3 \pi + 1 - 1} = 4x^{3 \pi}$

-Dan
• Sep 26th 2007, 05:01 PM
JonathanEyoon
For the second problem i'm a little confused. I just noticed that I canceled out an X in the beginning when they have different exponents. Was I able to do that?

The original problem is

4x^(3pi + 1) / x^2

I originally factored out an X since it is both in the numerator and denominator. I was able to do that right?

Well from your explanation, you still had an X in the numerator when I factored it out. mmmMMmm... i'm lost can you walk me through it :confused: Sorry to be such a pain
• Sep 26th 2007, 06:41 PM
JonathanEyoon

(a^(n+1))(3^(n+1)) / (a^n)(3^n) :p
• Sep 26th 2007, 06:44 PM
Jhevon
Quote:

Originally Posted by JonathanEyoon

(a^(n+1))(3^(n+1)) / (a^n)(3^n) :p

$\frac {a^{n + 1} \cdot 3^{n + 1}}{a^n \cdot 3^n} = \frac {(3a)^{n + 1}}{(3a)^n}$

the rest is trivial....whoa!, look at me, using the word "trivial." spoken like a true mathematician (Cool)
• Sep 26th 2007, 06:55 PM
JonathanEyoon
Quote:

Originally Posted by Jhevon
$\frac {a^{n + 1} \cdot 3^{n + 1}}{a^n \cdot 3^n} = \frac {(3a)^{n + 1}}{(3a)^n}$

the rest is trivial....whoa!, look at me, using the word "trivial." spoken like a true mathematician (Cool)

Hey Jhevon!

Ok from (3a)^ (n+1) / (3a)^n

I would cancel the (3a) out from both top and bottom leaving me with

(N+1) / N

N would cancel out which would result in the simplified form of 1 right?

Also can you help me out about my inquiries on post #6 :( i'm so confused with that problem. I'm trying to understand it.
• Sep 26th 2007, 06:58 PM
Jhevon
Quote:

Originally Posted by JonathanEyoon
Hey Jhevon!

Ok from (3a)^ (n+1) / (3a)^n

I would cancel the (3a) out from both top and bottom leaving me with

(N+1) / N

N would cancel out which would result in the simplified form of 1 right?

what?!!! how can you cancel bases and leave powers? that makes no sense. i guess it wasn't trivial after all.

use the fact that $\frac {x^a}{x^b} = x^{a - b}$

Quote:

Also can you help me out about my inquiries on post #6 :( i'm so confused with that problem. I'm trying to understand it.
lemme check ....use the same rule above for that question
• Sep 26th 2007, 07:14 PM
JonathanEyoon
(3a)^(n+1) / (3a)^n

so then the N will subtract out leaving

(3a) / (3a) which is 1?

*sigh* I forgot the rules and stuff for exponents since it's been a little while. =/
• Sep 26th 2007, 07:21 PM
Jhevon
Quote:

Originally Posted by JonathanEyoon
(3a)^(n+1) / (3a)^n

so then the N will subtract out leaving

(3a) / (3a) which is 1?

no. you would get 1 if you divided something by itself. that is not the case here. (3a)^{n + 1} is not the same as (3a)^n

Quote:

*sigh* I forgot the rules and stuff for exponents since it's been a little while. =/
i just told you the rule you should use, you don't need to remember anything.

$\frac {x^a}{x^b} = x^{a - b}$

here, your $x$ is $3a$, your $a$ is $n + 1$ and your $b$ is $n$. just plug into the formula
• Sep 26th 2007, 07:29 PM
JonathanEyoon
So then it'll be (3a)^(n+1-n)

For the other one,

4x^(3pi + 1) / x^2

If using the formula it would be

4x^(3pi + 1 - 2)

which would be 4x^(3pi - 1)

Did I do that right?
• Sep 26th 2007, 07:31 PM
Jhevon
Quote:

Originally Posted by JonathanEyoon
So then it'll be (3a)^(n+1-n)

For the other one,

4x^(3pi + 1) / x^2

If using the formula it would be

4x^(3pi + 1 - 2)

which would be 4x^(3pi - 1)

Did I do that right?

yes! (Clapping)
• Sep 26th 2007, 07:37 PM
JonathanEyoon
Thanks alot!!! I'm gonna do some research to online to see if i can get a more in depth look at exponents. I need to review!! Thanks again!