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Several simple exponent problems, Please help.

Hi, I am new to the forum. I have been stuck on a few math problems involving exponents for a while now and i don't know where else to turn.

I have attached a pdf file with my work and the questions i need help with are as follows. * These are not going to be marked and we were given most of the answers, so please explain to me and don't just give me the answer

**as you can see all the answers are already given so i'm not trying to cheat.. or be lazy and get people to work for me.. I benefit in no way whatsoever.**

**section a**

2.a) Okay the answer for this one is supposed to be 3 √1/32

But i don't understand how to arrive at this. I really don't even know where to start because i don't understand my teacher (currently working on switching teachers)

2.b) same as 2.a idk..

The rest i get

Then to **section B**

9.) i)

ii)

Please explain these. There are more i don't understand but i'm hoping by you explaining these to me i will be able to complete the rest.

Re: Several simple exponent problems, Please help.

Let's start with exercice 2.

2.a Multiply each side with $\displaystyle x^{\frac{1}{2}}$

2.b

$\displaystyle x^{\frac{1}{2}} +\frac{1}{2}x^{\frac{-1}{2}}(x-9)=0$

$\displaystyle \Leftrightarrow x^{\frac{1}{2}}+\frac{1}{2}x^{\frac{-1}{2}}x - \frac{9}{2}x^{\frac{-1}{2}}=0$

$\displaystyle \Leftrightarrow x^{\frac{1}{2}}+\frac{1}{2}x^{\frac{1}{2}}-\frac{9}{2}x^{\frac{-1}{2}}=0$

Same here, mulitply each side with $\displaystyle x^{\frac{1}{2}}$.

Re: Several simple exponent problems, Please help.

$\displaystyle \displaystyle x^{\frac{-3}{2}}-\frac{1}{9}x^{\frac{-1}{2}} = 0$

Make $\displaystyle \displaystyle x^{\frac{-1}{2}} = u$ then you have

$\displaystyle \displaystyle u^3-\frac{1}{9}u = 0 $ solve this cubic by factoring out $\displaystyle u$ then applying the difference of two squares.

You should get $\displaystyle \displaystyle u = 0, \frac{-1}{3}, \frac{1}{3} \implies x = \frac{1}{\sqrt{0}}, \frac{1}{\sqrt{\frac{-1}{3}}}, \frac{1}{\sqrt{\frac{1}{3}}}

$

Throw out the first two answers for reasons linked with the domain of the real numbers.

Re: Several simple exponent problems, Please help.

2. (a) I do not agree with your given solution. The expression will factor ...

$\displaystyle x^{-3/2} \left(1 - \frac{x}{9}\right) = 0$

$\displaystyle x = 9$ is the only solution.

2. (b) this expression will also factor ...

$\displaystyle x^{-1/2} \left(x + \frac{x-9}{2} \right) = 0$

$\displaystyle x = 3$ is the only solution

problem 9 follows the same procedure as problem 2 ...

9. (i) factor out $\displaystyle x^{-1/3}$

(ii) factor out $\displaystyle x(x+5)^{-1/2}$

Re: Several simple exponent problems, Please help.

For 2a the exponents are positive not negative as i view them with a magnifying glassand my answer is 1/9

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Re: Several simple exponent problems, Please help.

Quote:

Originally Posted by

**bjhopper** **For 2a the exponents are positive not negative** as i view them with a magnifying glassand my answer is 1/9

attached is a snapshot I copied ...

Re: Several simple exponent problems, Please help.

Thanks very much everybody. And sorry for the late reply.