1. waheguru

2. anonymous

|dw:1327615451961:dw|

3. anonymous

a negative index = 1 / positive eg x^-2 = 1/x^2

4. anonymous

the answer can also be written as 14x^-1 y^-5 ( x^-1 = 1/x)

5. waheguru

I still doont understanr

6. anonymous

hmm - my time is limited at moment - try the khanacademy site wahe - its got a good reputation

7. waheguru

why is the 14 positive its -2 x 7 = -14

8. JamesJ

$2x^{-4}y^{-3}(7x^3y^{-2})$ this is your expression?

9. waheguru

the 7 is negavive

10. JamesJ

$2x^{-4}y^{-3}(-7x^3y^{-2})$ is this it?

11. waheguru

can u help me do this one $4a^7b^5m^10(ten) (8a^9-b^-5m^2)+4a^7m^12/(2a^3bm^2)^5$

12. JamesJ

wait. Do you have the answer to your first question or not?

13. waheguru

yea i just forgot to put the - sigh but i dont get the way jimmy drew it why was the 14 over the other things|dw:1327617362311:dw|

14. JamesJ

Let's try it one more time. Your question then is: Simply this expression $2x^{-4}y^{-3}(7x^3y^{-2})$ correct?

15. waheguru

the 2 is negative ---the first one

16. waheguru

What do we do now?

17. JamesJ

So it's this: $-2x^{-4}y^{-3}(7x^3y^{-2})$ yes or no?

18. waheguru

yes

19. JamesJ

Right. First of all then, do you agree by the commutative property of multiplication, that we can reorder all of the terms and that $-2x^{-4}y^{-3}(7x^3y^{-2}) = (-2)7.x^{-4}x^3.y^{-3}y^{-2}$

20. waheguru

Yes

21. JamesJ

Good. Now we need to simplify each set of terms appropriately. (-2)7 = -14 that's straight forward I hope. What about $x^{-4}x^3$ what's that equal to?

22. waheguru

x$x-1???$

23. waheguru

x^-1

24. JamesJ

yes. And $y^{-3}y^{-2}$ is equal to what?

25. waheguru

y^-5

26. JamesJ

Yes, hence the answer is $-14x^{-1}y^{-5}$ which we can also write as $\frac{-14}{xy^5}$ that make sense?

27. waheguru

I dont get the bottom part

28. JamesJ

By definition $x^{-1}$ means and is equal to $\frac{1}{x}$

29. waheguru

Oh

30. JamesJ

Therefore also $y^{-5} = (y^5)^{-1} = \frac{1}{y^5}$

31. waheguru

SO if it has a power of -2 then the numerator is also 2???

32. JamesJ

in the denominator, yes. For instance $3^{-2} = \frac{1}{3^2}$ That makes good sense because, for example it makes this consistent: $3 = 3^1$ $= 3^{3-2}$ $= 3^3.3^{-2}$ $= 3^3 \frac{1}{3^2}$ $= 27 \frac{1}{9}$

33. waheguru

k

34. JamesJ

that last expression is 27 times 1/9 which is of course equal to 3.

35. JamesJ

Therefore $-14x^{-1}y^{-5} = - \frac{14}{xy^5}$

36. waheguru

Thankyou spoooooo much

37. waheguru

4a7b5m10(ten)(8a9−b−5m2)+4a7m12/(2a3bm2)5 can u help me with tis one

38. waheguru

$4a7b5m10(ten)(8a9−b−5m2)+4a7m12/(2a3bm2)5$

39. JamesJ

ok. good luck with your next one. Work it out patiently. Check it. Do it again. Iron out the errors. See if you can't figure it out. What's you've written is unreadable to me.

40. waheguru

oh ill write it again

41. waheguru

$4a^7b^5m^10(ten)(8a^9-b^-5m^2)+4a^7m^12)))divide by (2a^3bm^2)$

42. JamesJ

To get more than one thing in the exponent, use curly brackets. For example x^{10} $x^{10}$ To write a fraction, use \frac{a}{b} $\frac{a}{b}$