# Thread: Need help with multiply exponents!

1. ## Need help with multiply exponents!

Ok, watch the exponents in this problem, thanks!
How does (1+x)•2(√1+x)^½ = 2(√1+x)^3/2
when you multiply the following exponents (2)(-1/3) you get (-2/3).
Both are multiplying rational exponents, but two are doing it very differently. One has to be wrong, but which?

2. ## Re: Need help with multiply exponents!

Originally Posted by EJdive43
Ok, watch the exponents in this problem, thanks!
How does (1+x)•2(√1+x)^½ = 2(√1+x)^3/2
when you multiply the following exponents (2)(-1/3) you get (-2/3).
Both are multiplying rational exponents, but two are doing it very differently. One has to be wrong, but which?
(1+x)•2(√1+x)^½ = 2(√1+x)^3/2

I think you have one too many exponents.

correction ...

$(1+x) \cdot 2\sqrt{1+x} = (1+x) \cdot 2(1+x)^{1/2} = 2(1+x)^{3/2}$

3. ## Re: Need help with multiply exponents!

I understand that, but in a problem like (8x^3/4y^2)^ -1/3, where I'm ask to simplify, when I multiply the two exponents (2)(-1/3) I get 6/3 on on the answer sheet it says it's 2/3. http://www.wtamu.edu/academic/anns/m...ut5_ratexp.htm (example 5)

4. ## Re: Need help with multiply exponents!

Why did they multiply (2)(-1/3) to get (-2/3) when that not how you multiplied (1+x)*2(/1+x)^1/2 to get 3/2 as a result?

5. ## Re: Need help with multiply exponents!

Originally Posted by EJdive43
Why did they multiply (2)(-1/3) to get (-2/3) when that not how you multiplied (1+x)*2(/1+x)^1/2 to get 3/2 as a result?
${\left( {\frac{{8{x^3}}}{{4{y^2}}}} \right)^{\tfrac{{ - 1}}{3}}} = {\left( {\frac{{{y^2}}}{{2{x^3}}}} \right)^{\tfrac{1}{3}}} = \frac{{{y^{\tfrac{2}{3}}}}}{{{2^{\tfrac{1}{3}}}x}}$

6. ## Re: Need help with multiply exponents!

How did you work that out?

7. ## Re: Need help with multiply exponents!

Nvm I did, but how did you get 2/3 for y

8. ## Re: Need help with multiply exponents!

Originally Posted by EJdive43
Nvm I did, but how did you get 2/3 for y
$\left( 2 \right)\left( {\frac{1}{3}} \right) = \frac{2}{3}$

9. ## Re: Need help with multiply exponents!

Don't you multiply the exponents which means your going to add? For example, (2)(-1/3) we will add the exponents which will be written as 2+-1/3, right? Isn't that what Skeeter did with the equation above?

10. ## Re: Need help with multiply exponents!

Originally Posted by EJdive43
Don't you multiply the exponents which means your going to add? For example, (2)(-1/3) we will add the exponents which will be written as 2+-1/3, right? Isn't that what Skeeter did with the equation above?
$\text{It is a rule that }{\left( {{x^a}} \right)^b} = {x^{ab}}\text{ so applying that rule we get }\left( {{y^2}} \right)^{\frac{1}{3}}} = {y^{\frac{2}{3}}}~.$

11. ## Re: Need help with multiply exponents!

do you understand that

$x^a \cdot x^b = x^{a+b}$ and $(x^a)^b = x^{ab}$

are two completely different rules for exponents?