Solving Simple Index Questions with Brackets and Fractions

[lloydowen]

Simple Indicies Question [SOLVED]

Homework Statement

I'm having a little problem with indicies, I know it's simple for someone with a lot of question.

So I'm wondering what to do first in this question, brackets or should I multiply out the fractions inside the brackets?

I have to simplify it that's all :)

Homework Equations

The Attempt at a Solution

I don't have an attempt yet sorry :(

 

[micromass]

I'd start by working out the inside of the brackets first. I think that'll be the easiest.

 

[lloydowen]

Thanks for the reply, so when I worked it out and simplified it first I got (x^2.5 x^2 x^-3)^2 which would equal to something like x^3, but in derive the answer is x^17..

What am I doing wrong :(?

 

[micromass]

I got (x^2.5 x^2 x^-3)^2

That X^-3 isn't correct, is it??

 

[lloydowen]

Well I thought it was... What else could it be? I wish I had a good course tutor in College, I literally teach myself almost everything! *try*

 

[Ray Vickson]

Well I thought it was... What else could it be? I wish I had a good course tutor in College, I literally teach myself almost everything! *try*

You have $$F = \left( \frac{X^4 X^5 X}{X^{1.5} X^3 X^{-3}}\right)^2 .$$ The first step is to simplify the quantity inside the bracket, to obtain $F = (X^a)^2.$ So, the first order of business is to figure out what is 'a' in the following:
$$\frac{X^4 X^5 X}{X^{1.5} X^3 X^{-3}} = X^a.$$ After that, the rest is easy: $(X^a)^2 = X^{2a} .$

RGV

 

[lloydowen]

Sorry, common mistake, so it would be X^3?

 

[lloydowen]

Here's what I got... That previous post is very complicated

 

[Mentallic]

You need to slowly apply these rules, you keep making mistakes.

$$a^b\cdot a^c=a^{b+c}$$

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

$$\left(a^b\right)^c=a^{bc}$$

 

[micromass]

How is $X^{-3}$ defined?? What is $\frac{X}{X^{-3}}$??

Are you aware of the identity $\frac{a^n}{a^m}=a^{n-m}$??

 

[lloydowen]

Thanks guys I have solved this problem now :) I will keep going over and over until I get it perfect.

 

[Mentallic]

Could you show us just to be sure? Because two wrongs can sometimes accidentally make a right

And assuming you used the formulae correctly, just a tip, it'll probably be easier if you simplify the numerator first, then the denominator, then apply the quotient rule.

 

[lloydowen]

What I did first was simplify the insides of the brackets. To do this I applied the 2nd law of indicies and take away the denominator from the numerator for example, first of all I got x^2.5 because 4-1.5 = Positive 2.5... Then the same for the next one in the brackets.

Now the last fraction in the equation at first I forgot the rule of two the same signs make positive and the opposite signs make a negative. So x-(-3) would be equal to x^3.

Then once I got all of them, I added them up to form (x^7.5)^2

(x^7.5)^2
=x^17

 

[Ray Vickson]

What I did first was simplify the insides of the brackets. To do this I applied the 2nd law of indicies and take away the denominator from the numerator for example, first of all I got x^2.5 because 4-1.5 = Positive 2.5... Then the same for the next one in the brackets.

Now the last fraction in the equation at first I forgot the rule of two the same signs make positive and the opposite signs make a negative. So x-(-3) would be equal to x^3.

Then once I got all of them, I added them up to form (x^7.5)^2

(x^7.5)^2
=x^17

OK, that works, but you still have made some errors. However, what people are suggesting is that you do it more systematically, by simplifying the numerator and denominator separately:
$$\mbox{numerator} = X^4 X^5 X = X^{4+5+1} = X^{10}$$ and
$$\mbox{denominator} = X^{1.5} X^3 X^{-3} = X^{1.5 + 3 - 3} = X^{1.5},$$ to get $$\mbox{ratio} = \frac{\mbox{numerator}}{\mbox{denominator}} = \frac{X^{10}}{X^{1.5}} = X^{10 - 1.5} = X^{8.5}.$$ There is less chance of making an error when you do it this way.

RGV

 

[lloydowen]

Oh right I see what you mean! I told you my Tutor was rubish :P I'll get into that routine then, Thank you! :)

 

[Mentallic]

(x^7.5)^2
=x^17

How did you get from (x^7.5)²=x¹⁷?

 

[lloydowen]

How did you get from (x^7.5)²=x¹⁷?

Ah Sorry I must of confused my self somewhere... I meant x^8.5 at least that's what I have on paper..

 

[Mentallic]

Ahh ok just a typo then, because you did it twice

 

[lloydowen]

Lmao not sure why I did it twice, I was very tired that night :P