## bleuspectre one year ago Simplify (3x^3y^4)^2/(6x^5y^3)(x^3y^2)^4 1/x^7y^3 3/2x^11y^3 3x^11y^3/2 9x^6/y^3

1. Nnesha

familiar with the exponent rules ?

2. bleuspectre

Not much :/

3. Nnesha

alright exponent rules $\huge\rm (ab)^m =a^mb^m$ numbers/variables in the parentheses raised by m power when we multiply same bases we should add exponents $\huge\rm x^m \times x^n=x^{m+n}$ and when we divide same base , subtract their exponents $\huge\rm \frac{ x^m }{ x^n }=x^{m-n}$

4. Nnesha

$\huge\rm \frac{ \color{ReD}{(3x^3y^4)^2}}{(6x^5y^3)(x^3y^2)^4}$ start with first exponent rule i posted above

5. Nnesha

$\huge\rm {(3x^3y^4)^2} = ??$

6. bleuspectre

Would it be (3x^5y^6)?

7. bleuspectre

I'm not good at math :/

8. Nnesha

multiply the exponents

9. Nnesha

you will be one day

10. Nnesha

exponent rules $\huge\rm (a^1b^1)^m =a^{1 \times m}b^{1 \times m}$ numbers/variables in the parentheses raised by m power according to this rule $\huge\rm {(3x^3y^4)^2} = 3^3 x^{3 \times2}y^{4 \times3}$ every number/variable in the parentheses raised by 2 power multiply the exponents

11. bleuspectre

3^3x^6y^12

12. Nnesha

sorry there is a typo $\huge\rm {(3x^3y^4)^2} = 3^2 x^{3 \times2}y^{4 \times3}$ 3 to the 2 power not 3

13. bleuspectre

Ok

14. Nnesha

the power tells us how many times we should multiply the base 3^2 = 3 times 3

15. bleuspectre

Ok

16. Nnesha

ugh typo sorry there is a typo $\huge\rm {(3x^3y^4)^2} = 3^2 x^{3 \times2}y^{4 \times2}$ 3 to the 2 power not 3 and y^4 times 2 not 3 now simplify that

17. bleuspectre

$(3x ^{3}y ^{4})^{2} = 3^{2}x ^{6}y ^{8}$

18. Nnesha

yes right what about 3^2 = ?

19. bleuspectre

9

20. Nnesha

yes right so $\huge\rm \frac{ \color{ReD}{9x^6y^8}}{(6x^5y^3)(x^3y^2)^4}$ now apply the same exponent rule for (x^3y^2)^4

21. bleuspectre

Would i combine them?

22. Nnesha

apply the exponent rule just like we did for the numerator

23. bleuspectre

Because I got $x ^{12}y ^{8}$

24. bleuspectre

would I multiply the 4 to the other one too?

25. Nnesha

no bec 4 is power of x^3 y^2 so that's it for this part $\huge\rm \frac{ \color{black}{9x^6y^8}}{(6x^5y^3)x^{12}y^{8}}$ you can remove the parentheses from (6x^5y^3) bec there isn't any exponent outside the parentheses $\huge\rm \frac{ \color{black}{9x^6y^8}}{6x^5y^3x^{12}y^{8}}$ now apply the 2nd exponent rule ~when we multiply same bases we should add exponents $\huge\rm x^m \times x^n=x^{m+n}$

26. bleuspectre

$6x ^{17}y ^{11}$

27. Nnesha

nice $\huge\rm \frac{ \color{black}{9x^6y^8}}{6x^{17}y^{11}}$ reduce the fraction 9/6 and apply the exponent rule when we divide same base , subtract their exponents $\huge\rm \frac{ x^m }{ x^n }=x^{m-n}$

28. bleuspectre

3x^11y^3/2

29. Nnesha

hmm top exponent minus bottom exxponents so 6-17 = ?

30. bleuspectre

oh -11 and -3

31. Nnesha

yes right now we need to change negative to positive exponent $\huge\rm x^{-m}=\frac{ 1 }{ x^m }$ to convert negative to positive exponent u should flip the fraction , when you flip it the sign of the exponent would change

32. bleuspectre

So 3/2x^11y^3

33. Nnesha

looks good

34. bleuspectre

Thank you so much!

35. Nnesha

np good work you just need to practice more on this stuff then you will be an expert at exponent rules

36. bleuspectre

I will keep practicing, thank you again.

37. Nnesha

o^_^o