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all x terms right?

\[5^{-1/2}*5x ^{5/2}(5x)^{-3/2}\]

All in x terms.

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|

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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