## anonymous one year ago Medal! Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator.

1. anonymous

$4m^\frac{ 4 }{ 3 }*m^\frac{ -7 }{ 4 }$

2. Nnesha

$\huge\rm x^m \times x^n = x^{m+n}$ exponent rule! when u multiply same bases you should ad their exponents

3. anonymous

i don't now how to add the fractions. because they've got different denominators

4. Nnesha

multiply them

5. Nnesha

$\frac{ 4 }{ 3 } + \frac{ -7 }{ 4 } = \frac{ ? }{ 3(4) }$

6. anonymous

$\frac{ -28 }{ 12 }$

7. Nnesha

|dw:1433698357618:dw| 4 and 3 are the denominator first fraction doesn't have 4 at the denominator so multiply 4 times 4 2nd fraction -7 doesn't have 3 at the denominator so multiply it by 3 same like cross multiplication but don't forget the signs

8. anonymous

which equals$\frac{ 7}{ 3 }$

9. anonymous

wait, what?

10. anonymous

i just realized, because they're exponents, wouldn't i be adding the fractions, not multiplying?

11. Nnesha

yes add $\frac{ 4 }{ 3 } \color{Red}{+} \frac{\color{blue}{ -}7 }{ 4 } = \frac{ 4 }{3 } \color{reD}{-}\frac{7}{4}$ here positive times negative = negative now 3 and 4 both are common denominator

12. Nnesha

the*

13. Nnesha

yes add $\frac{ 4 }{ 3 } \color{Red}{+} \frac{\color{blue}{ -}7 }{ 4 } = \frac{ 4 }{3 } \color{reD}{-}\frac{7}{4}=\frac{????}{3(4)}$ now cross multiply don't forget the negative sign |dw:1433698871386:dw|

14. anonymous

$\frac{ 28 }{ 12 }$

15. anonymous

that's what i got before but that's when you're multiplying it and they need to be added because they're exponents.

16. Nnesha

how did you get 28?

17. Nnesha

|dw:1433699227333:dw| or in other words multiply first fraction by 4 and 2nd fraction by 3

18. Nnesha

$\frac{ 4 }{ 3 } \color{Red}{+} \frac{\color{blue}{ -}7 }{ 4 } = \frac{ 4 }{3 } \color{reD}{-}\frac{7}{4}= \frac{4(4) - 3(7)}{3(4)}$ like this

19. anonymous

$\frac{ 16-21 }{ 12 }$

20. anonymous

$\frac{ -5 }{ 12 }$

21. anonymous

like that?

22. Nnesha

yes that's right so $\large\rm 4m^\frac{ 4 }{ 3 }*m^\frac{ -7 }{ 4 } = ???$

23. anonymous

$4m^\frac{ -5 }{ 12 }$

24. Nnesha

yep right now there is another exponent rules $\huge\rm x^{-m} = \frac{ 1 }{ x^m }$

25. anonymous

yup. got that. thank you!

26. Nnesha

np :-)