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

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

Mathematics
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all x terms right?
\[5^{-1/2}*5x ^{5/2}(5x)^{-3/2}\]
All in x terms.

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Other answers:

firt add the power of x as 5 is common base 5/2-3/2 The total answer you will get x/sqrt(5)
Congrats! Correct answer!
Thank you.
O wait.... the answer is sqrt(5)x
oh. How do I get there?
|dw:1440210052094:dw|
initial one above, I think you got that... Now see what happens
|dw:1440210109054:dw|
as 5^-1/2 is sqrt(5) in the denominator (Law of exponents)
now sqrt5*sqrt5=5 so simplify
|dw:1440210183235:dw|
I do it this way: \[5^{-1/2}*5x ^{5/2}(5x)^{-3/2}= 1/5*\sqrt{5x ^{5}}(1/\sqrt{5x ^{3}})\]
Got it?
My way is easier.........
I do not understand how I get from |dw:1440210294618:dw|
I then get this|dw:1440210396554:dw|
Is that work correct? If so, then I get |dw:1440210462464:dw|
In simple words, when base is same in this case 5 is same, you can subtract the powers!
So you are saying that I can go from |dw:1440210540555:dw|
Your reasoning would be correct if the exponents were not negative? I do not understand how people can get to the answer 5sqrtx
No No!
-1/2 dont do that!
only 5/2-3/2 1/2 has no x term
It is still incorrect though because it would be 5/2-(-3/2)=8/2
ofcourse!
its 5/2+(-3/2) =2/2=1
now are you understanding?
oh.let me try this now.|dw:1440211147039:dw|
I understand the logic. Where doe the 5^-1/2 go now?
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?
Yes. So what is the final answer?
|dw:1440211406218:dw|
|dw:1440211455166:dw| so sqrt(5)x is the answer
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