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

- anonymous

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

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- arindameducationusc

all x terms right?

- anonymous

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

- anonymous

All in x terms.

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## More answers

- 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)

- arindameducationusc

Congrats! Correct answer!

- anonymous

Thank you.

- arindameducationusc

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

- anonymous

oh. How do I get there?

- arindameducationusc

|dw:1440210052094:dw|

- arindameducationusc

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

- arindameducationusc

|dw:1440210109054:dw|

- arindameducationusc

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

- arindameducationusc

now sqrt5*sqrt5=5
so simplify

- arindameducationusc

|dw:1440210183235:dw|

- anonymous

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

- arindameducationusc

Got it?

- arindameducationusc

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

- anonymous

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

- anonymous

I then get this|dw:1440210396554:dw|

- anonymous

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

- arindameducationusc

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

- anonymous

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

- anonymous

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

- arindameducationusc

No No!

- arindameducationusc

-1/2 dont do that!

- arindameducationusc

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

- anonymous

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

- arindameducationusc

ofcourse!

- arindameducationusc

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

- arindameducationusc

now are you understanding?

- anonymous

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

- anonymous

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

- 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?

- anonymous

Yes. So what is the final answer?

- arindameducationusc

|dw:1440211406218:dw|

- arindameducationusc

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

- arindameducationusc

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

- arindameducationusc

@TotallyNautical are you there?

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