# Thread: Confirmation/aid for simplifying algebraic indices

1. ## Confirmation/aid for simplifying algebraic indices

Hello everyone.
I have yet another pile of mathematics homework, and currently working on it. I need some confirmation and, if so, help on the following - can they be simplified any more than I have done?

1. $\displaystyle (6v^4)^2$
= $\displaystyle 6^2 X (v^4)^2$
= $\displaystyle 6^2 X v^8$
= $\displaystyle 36v^8$ Is this correct?

2. $\displaystyle (a^3b^3) ^2$
= $\displaystyle a^6b^6$ ?

3. $\displaystyle (mn^4)^3$
= $\displaystyle mn^12$

4. $\displaystyle a^2b^3 X ab^2$
= I am not sure on this...

5. $\displaystyle r^5s^2 / r^2s$
= Explanation and guidance on this one...

6. $\displaystyle (3m^2m^2) X 2n^2$
= Same as #5

Thank you so much to all who help me in this dilemma!

I was just wondering, how soon is someone due to reply? I am in need of some explanations soon to help me work through these. Thank you.

1. $\displaystyle (6v^4)^2=6^2Xv^{4X2}=36v^8$

2. $\displaystyle (a^3b^3) ^2=a^{3X2}Xb^{3X2}=a^6Xb^6$

3. $\displaystyle (mn^4)^3=m^3Xn^{4X3}=m^3n^{12}$

4. $\displaystyle a^2b^3 multiplied by (X) ab^2 = a^2Xb^3XaXb^2=a^{2+1}b^{3+2}$

5. $\displaystyle r^5s^2 / r^2s= r^{5-2}s^{2-1}=r^{3}s$

6. $\displaystyle (3m^2m^2) multiplied by (X) 2n^2= 3m^{2+2}X2n^2=6m^4n^2$

P.S. I have discovered a new technique as you can see!--Welldone
Check the quoted thing

3. Hi, ADARSH, my new buddy!

Is the steps or answers in the quote? Thank you for either!

Is the steps / answers in the quote? Thank you for either!
Yep my new buddy
Formulae
--$\displaystyle x^a Xx^b= x^{a+b}$

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

--$\displaystyle (x^a)^b=x^{aXb}$

5. Well, I guess we have reached the end of this post, ADARSH. I thank you for your help and explanations (I really appreciate the formulae too, it adds to my mathematic knowledge. Did you remember it by memory or do you have it nearby on a piece of paper?).

Best wishes and good luck (and may we meet again),

Did you remember it by memory or do you have it nearby on a piece of paper?).
Hey Jade , Remember that you need to remember these formulae if you want to solve questions of maths

ADARSH, just checking, did you realise that in $\displaystyle r^5s^2 / r^2s$, the / is a divided sign?
ADARSH, just checking, did you realise that in $\displaystyle r^5s^2 / r^2s$, the / is a divided sign?
$\displaystyle \frac{r^5s^2}{r^2s} = \frac{r^3}{s}$