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