## anonymous one year ago Simplify 12 to the 3rd over 12 to the 7th. 12^4 1 over 12 to the 4th 1 over 12 to the negative 4th 12^10

1. anonymous

@phi

2. phi

$\frac{12^3}{12^7}$ any idea what $\frac{12}{12}$ is ?

3. anonymous

12/12 would equal to 1 right?

4. phi

yes. as you know , when you multiply fractions you multiply top times top and bottom times bottom, right ?

5. anonymous

ya top and top bottom and bottom

6. phi

$\frac{12\cdot 12\cdot 12}{12\cdot 12\cdot 12} \cdot \frac{1}{12\cdot 12\cdot 12\cdot 12}$ do you see that is 12^3 / 12^7 ?

7. anonymous

yes

8. phi

do you also see the first part can be simplified? something divided by itself is what ?

9. anonymous

hmm

10. anonymous

i dont see what can be divided

11. phi

or perhaps you should notice $\frac{12\cdot 12\cdot 12}{12\cdot 12\cdot 12} = \frac{12}{12} \cdot \frac{12}{12} \cdot \frac{12}{12}$

12. anonymous

mmmm

13. anonymous

if they got multiplied together and divided? maybe??

14. phi

the right side, if you multiply tops you get 12*12*12 and ditto for the bottom. both sides mean the same thing but what is 12/12 if you simplify first?

15. anonymous

12/12 simplified is 1

16. phi

and what is 1*1*1? it is 1 $\frac{12\cdot 12\cdot 12}{12\cdot 12\cdot 12} = \frac{12}{12} \cdot \frac{12}{12}\cdot \frac{12}{12} = 1 \cdot 1 \cdot 1$ (12*12*12)/(12*12*12) is an example of something (in this case 12*12*12) divided by itself. you get 1

17. anonymous

ohhh

18. anonymous

ok

19. phi

so simplify $\frac{12\cdot 12\cdot 12}{12\cdot 12\cdot 12} \cdot \frac{1}{12\cdot 12\cdot 12\cdot 12}$

20. anonymous

1/12^4?

21. anonymous

because the 4 12?

22. phi

and the first part (12*12*12)/(12*12*12) is just 1 and when we multiply by 1 we can ignore it. so yes 1/12^4

23. anonymous

alrighty:D

24. anonymous

and im taking it as 1/12^4 is the answer also?

25. phi

the short cut is subtract top exponent minus bottom exponent $\frac{12^3}{12^7} = 12^{3-7} = 12^{-4} = \frac{1}{12^4}$

26. anonymous

ohhhh

27. anonymous

let me take a pic of thats because thats useful

28. anonymous

ok thats it

29. anonymous

let me submmit it

30. anonymous

your the best we got a 100%

31. anonymous

thanks man your the best if i could rate you id give u a million stars xD

32. phi

yw

33. anonymous

OK THANKS MAN BYE!!