## haltiamali 2 years ago (2a^3b^2) (b^3)^2 Simplify. (The ^'s mean to the power of..)

1. ajprincess

$$\large (x^y)^z)=x^{y*z}$$ using this can u simplify $$\large (b^3)^2$$?

2. haltiamali

So it would be $b^6..?$

3. ajprincess

ya very good:)

4. ajprincess

$$\large x^y*x^z=x^{y+z}$$ Usin this can u simplify $$\large b^2*b^6$$?

5. haltiamali

Is the answer $2a^5b^12$

6. haltiamali

that last number is supposed to be a 12

7. ajprincess

nope. $$\large x^y*x^z=x^{y+z}$$ using this hint can u simplify $$\large b^2*b^6$$?

8. haltiamali

$b^8?$

9. ajprincess

ya very good:)

10. haltiamali

$2a^3b^8$ is the answer?

11. ajprincess

yup:)

12. haltiamali

thx. :) can you help me with the other 3?

13. ajprincess

ya sure:)

14. haltiamali

$(-4xy)^3 (-2x^2)^3$

15. ajprincess

$$\Large (-2x^2)^2=(-2)^2*(x^2)^2$$ What is $$\Large (-2)^2$$?

16. haltiamali

4

17. ajprincess

ya good:) What do u get when u simplify $$\Large (x^2)^2$$?

18. haltiamali

4x?

19. ajprincess

nope $$\Large (a^b)^c=a^{b*c}$$ using this simplify $$\Large (x^2)^2$$

20. haltiamali

ohh. $x^4$ right?

21. ajprincess

ya:) $$\Large(-4xy)^3=(-4)^3*(x^1)^3*(y^1)^3$$ Nw can u simplify (-4)^3*(x^1)^3*(y^1)^3\)

22. haltiamali

-64 x^4 y^4?

23. haltiamali

oh wait

24. haltiamali

hahaha I get it :D

25. haltiamali

$(-14xy^4) (-1/2xy^3)$

26. haltiamali

that's negative half

27. haltiamali

Would it be $-14 1/2 x+y^7?$

28. ajprincess

wait a sec. oops sorry it is $$\Large (-2x^2)^3$$ right? So $$\Large (-2x^2)^3=(-2)^3*(x^2)^3$$ We r nt yet done with our previous problem. so it will be better if we finish that and come to this one. What is $$(-2)^3)? What do u get when u simplify \((x^2)^3$$?

29. haltiamali

$(-2x^6)$ right?

30. ajprincess

$$\Large (x^2)^3=x^6$$ that's right:) but what is $$\Large (-2)^3=? 31. haltiamali oh -8 32. ajprincess ya:) so \(\Large (-2x^2)^3=-8x^6$$ Nw $$\Large(-4xy)^3=(-4)^3*(x^1)^3*(y^1)^3$$ What is $$\Large (-4)^3=$$? What do u get when u simplify $$\Large (x^1)^3$$ and $$\Large (y^1)^3$$?

33. haltiamali

-64 x^4 and y^4

34. ajprincess

$$\Large(a^b)^c=a^{b*c}$$ usin this general rule only u have to simplify $$(x^1)^3$$ and $$(y^1)^3$$

35. haltiamali

oh. x^3 and y^3

36. ajprincess

ya good:)

37. ajprincess

$$\Large(-4xy)^3=-64x^3y^3$$ $$\Large(-2x2)^3=-8x^6$$ $$\Large(-64x^3y^3)*(-8x^6)=(-64*8)*(x^3*x^6)*y^3$$ To simplify $$\Large(x^3*x^6)$$ u have to use the general rule $$\Large(a^b)*(a^c)=a^{b+c}$$

38. ajprincess

Can u figure out the final answer @haltiamali

39. haltiamali

yes :) tysm

40. ajprincess

k nw moving on to ur next problem $(-14xy^4)(\frac{ -1 }{ 2 }xy^3)=(-14*-\frac{ 1 }{ 2 })(x^1*x^1)*(y^4*y^3)$ See if u can simplify nw. If u find any difficulties while solving pls do ask:)

41. haltiamali

Thanks ! :)

42. ajprincess

Welcome:)