kandsbbf
What is a simpler form of the radical expression?



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kandsbbf
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dw:1358117374152:dw

kandsbbf
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@Butterfly16

kandsbbf
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some pls help

kandsbbf
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@loveudrew123

nooce
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Simplify the x^12 and y^16 first

nooce
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Remember:\[(x^a)^b x^{a• b}\]

kandsbbf
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do i just simplify the exponents?

nooce
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We're simplifying them first, cause it's easier haha, we'll move on to the 240 after you simplify the exponents

nooce
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2901*

kandsbbf
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so how do i simplify them?

nooce
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Well since, \[(x^a)^b = x^{a•b}\]
divide x^12 and y^16 by 4. What do you get?

nooce
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(I mean the powers of x and y)

kandsbbf
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x^2 x^4

nooce
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Wait, but 12/4 = 3, not 2.
Also, it would be y^4

nooce
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But moving on,
now we simplify
\[\sqrt[4]{2901}\]
Do you have any idea on how to do this? (just asking)

kandsbbf
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no lol, but i really appreciate u teaching me

nooce
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No problem, I'm glad to help :)
Well, first, we need to find a factor of 2901 that is a power of 4.
(ex. 16, because 2^4 = 16)

kandsbbf
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how do we do that lol

nooce
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Here's a list of em:
\[2^4 = 16\]
\[3^4 = 81\]
\[4^4 = 256\]
\[5^4 = 625\]
\[6^4 = 1296\]
Are any of these numbers factors of 2901?

kandsbbf
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no i get dec. for all of them

nooce
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The number in the problem is 2901, right?

nooce
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Or is it 2401?

nooce
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because,
\[7^4 = 2401\]

kandsbbf
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2401 sorry(:

kandsbbf
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@nooce

nooce
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Alright, since we know 2401 = 7^4, we can take that out of the radical :)
So we get,
\[\sqrt[4]{2401x^{12}y^{16}} = 7x^3y^4\]
Do you get it? :D

kandsbbf
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yes thankyou!