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Find the following assuming that a can represent any real number
\[\sqrt[4]{(5a)}^{4}\]
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gandalfwiz
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5a, because ur taking the 4 root of something to the fourth power
mathtard
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so why would it be 5a?
polpak
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it's actually |5a|
gandalfwiz
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<rolls eyes>
polpak
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radicals are to exponents as division is to multiplication.
polpak
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So if you take the 4th root of something to the 4th power you will get what you started with (except with even roots you have to slap an absolute value on it)
polpak
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Or even powers that is
mathtard
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so I don't understand what the lines represent on the sides of the answer?
polpak
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Absolute value sign.
mathtard
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so the 4's basically cancel eachother out?
gandalfwiz
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xactely
polpak
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Yes.
polpak
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If you have the same power as you have index on your radical it cancels out the exponent.
mathtard
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ok I think I understand. at least better. But what are the lines on each side for?
polpak
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It's a nit picky detail.
polpak
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| | is the absolute value operator.