## greeneyes<3 2 years ago Help! Simplify: 1. (-z)^3(3z^4) 2. 5(x^2z^6)^3(5x^2z^6)^-3 Thank you!:)

1. jim_thompson5910

what does (-z)^3 simplify to

2. greeneyes<3

-z? I don't know... :/

3. jim_thompson5910

close

4. jim_thompson5910

(-z)^3 = (-1*z)^3 (-z)^3 = (-1)^3*(z)^3 (-z)^3 = -1*z^3 (-z)^3 = -z^3

5. jim_thompson5910

(-z)^3(3z^4) turns into -z^3*3z^4

6. jim_thompson5910

what's next?

7. greeneyes<3

add the z's but the negative is still messing me up :/

8. jim_thompson5910

think of -z^3*3z^4 as -1z^3*3z^4

9. jim_thompson5910

so the coefficients are -1 and 3, they multiply to -1*3 = -3

10. jim_thompson5910

z^3 times z^4 = z^(3+4) = z^7 so the final answer is -3z^7

11. greeneyes<3

thank you! :) can you help me with the second one as well?

12. jim_thompson5910

how far did you get with it?

13. greeneyes<3

does exponents distribute first? if so, does the ^3 distribute to the 5 as well or just the (x^2z^6)?

14. jim_thompson5910

the exponent of 3 only applies to terms inside the parenthesis

15. jim_thompson5910

so (x^2z^6)^3 means you cube x^2 and z^6

16. greeneyes<3

I got 1/25 after simplifying

17. jim_thompson5910

let me check

18. jim_thompson5910

you are correct

19. greeneyes<3

thank you for helping me! :) you're the best! :)

20. jim_thompson5910

you're welcome