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Exponents and Roots

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Exponents and Roots

by davo45 » Sun Mar 06, 2011 6:03 am
Solve using the properties of roots:

(4sqroot(64))/(4sqroot(4))

= 4sqroot (16)

= 2

Understand how to get to 2, but could someone explain mathmatically how to go from 4sqroot (16) to 2.

thank you.
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by vineeshp » Sun Mar 06, 2011 7:17 am
I am not sure I understand your question. :(

Do u mean 4th root? 4 multiplied by sqrt(64)?

I think it is high time BTG brought in an equation editor into the post editor.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by vineeshp » Sun Mar 06, 2011 7:25 am
(4sqroot(64))/(4sqroot(4))
Assuming you meant 4th root cos u cannot get to 2 otherwise.

My way of solving would be

4th root of (4^3)/4th root of (4)

(4^(3/4))/(4^(1/4))


applying a^x/a^y = a^(x-y)

(4^(3/4))/(4^(1/4)) = (4^((3/4)-(1/4))) = 4^(2/4) = 4^(1/2) or square root of 4 which is 2.

===============================================================

OR.

4th root of 64/4th root of 4
=4th root of 64/4
=4th root of (16)
=4th root of (2^4)
=2^(4/4)
=2^1 = 2
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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