How to simplify the expression... X^3(2yz^2)^3?

Question

please help me.

This is some of my summer work for when school starts again and I cant remember how to do it.

Answer 1

I'm not that good in solving those problems BUT I've got the answers for each, here they go: (in order)

  

8x^3 ·y^3 ·z^6

10·x^4

12·x^2

these are my steps:

x^3·(2·y·z^2)^3

take care of the brackets first

x^3·(2^3·y^3·z^6) (everything inside ·^3, ^2·^3=^6, 2^3=8)

should be 8x^3·y^3·z^6

the second problem:

(2/3x^-3)·(15x^7)

2/3·15=10

x^-3·x^7 <- if the variable is the same ( x here) you can sum (-3+7=4)

therefore, the simplified problem is 10x^4

last problem

(3x^3)·(4x^5)/(x^2)^3

the first part (3x^3)·(4x^5) simplifies to 12x^8 (3·4=12 and ^3+^5)

and the latter part

simplifies to x^6 (^2·^3=^6)

the problem looks like this now: 12x^8/x^6

further simplified like this: 12x^2 (^8/^6 is like 8+(-6) or something)

I checked my solutions with derive and they seem alright

hope I'm right and didn't confuse you, ha ha oh god I hate math >_<

well good luck in finding the solution, the nerds should arrive soon ;)