## anonymous one year ago Simplify (5)^-1/2 * (5x)^5/2 (5x)^-3/2 My final answer is x/sqrt5. Is this correct?

1. arindameducationusc

all x terms right?

2. anonymous

$5^{-1/2}*5x ^{5/2}(5x)^{-3/2}$

3. anonymous

All in x terms.

4. arindameducationusc

firt add the power of x as 5 is common base 5/2-3/2 The total answer you will get x/sqrt(5)

5. arindameducationusc

6. anonymous

Thank you.

7. arindameducationusc

O wait.... the answer is sqrt(5)x

8. anonymous

oh. How do I get there?

9. arindameducationusc

|dw:1440210052094:dw|

10. arindameducationusc

initial one above, I think you got that... Now see what happens

11. arindameducationusc

|dw:1440210109054:dw|

12. arindameducationusc

as 5^-1/2 is sqrt(5) in the denominator (Law of exponents)

13. arindameducationusc

now sqrt5*sqrt5=5 so simplify

14. arindameducationusc

|dw:1440210183235:dw|

15. anonymous

I do it this way: $5^{-1/2}*5x ^{5/2}(5x)^{-3/2}= 1/5*\sqrt{5x ^{5}}(1/\sqrt{5x ^{3}})$

16. arindameducationusc

Got it?

17. arindameducationusc

My way is easier.........

18. anonymous

I do not understand how I get from |dw:1440210294618:dw|

19. anonymous

I then get this|dw:1440210396554:dw|

20. anonymous

Is that work correct? If so, then I get |dw:1440210462464:dw|

21. arindameducationusc

In simple words, when base is same in this case 5 is same, you can subtract the powers!

22. anonymous

So you are saying that I can go from |dw:1440210540555:dw|

23. anonymous

Your reasoning would be correct if the exponents were not negative? I do not understand how people can get to the answer 5sqrtx

24. arindameducationusc

No No!

25. arindameducationusc

-1/2 dont do that!

26. arindameducationusc

only 5/2-3/2 1/2 has no x term

27. anonymous

It is still incorrect though because it would be 5/2-(-3/2)=8/2

28. arindameducationusc

ofcourse!

29. arindameducationusc

its 5/2+(-3/2) =2/2=1

30. arindameducationusc

now are you understanding?

31. anonymous

oh.let me try this now.|dw:1440211147039:dw|

32. anonymous

I understand the logic. Where doe the 5^-1/2 go now?

33. arindameducationusc

its a constant so its just 1/sqrt(5) see, 5^1/2 = sqrt(5) so 5^-1/2=1/sqrt(5) Did you get the logic?

34. anonymous

Yes. So what is the final answer?

35. arindameducationusc

|dw:1440211406218:dw|

36. arindameducationusc

|dw:1440211455166:dw| so sqrt(5)x is the answer

37. arindameducationusc

If you liked my response, don't forget to medal and fan....

38. arindameducationusc

@TotallyNautical are you there?