1. ## Exponents

We've been on exponents for a little while now in class and I keep getting confused . 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 =)

2. Originally Posted by JonathanEyoon
We've been on exponents for a little while now in class and I keep getting confused . 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

3. 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

4. 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 .

((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 ?

5. 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 .

((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.

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

-Dan

6. 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 Sorry to be such a pain

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

8. Originally Posted by JonathanEyoon

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

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

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

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

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.

10. 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 $\displaystyle \frac {x^a}{x^b} = x^{a - b}$

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

11. (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. =/

12. 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

*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.

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

here, your $\displaystyle x$ is $\displaystyle 3a$, your $\displaystyle a$ is $\displaystyle n + 1$ and your $\displaystyle b$ is $\displaystyle n$. just plug into the formula

13. 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?

14. 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!

15. 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!