Question

Find the following assuming that a can represent any real number
\[\sqrt[4]{(5a)}^{4}\]

Answer 1

5a, because ur taking the 4 root of something to the fourth power

Answer 2

so why would it be 5a?

Answer 3

it's actually |5a|

Answer 4

<rolls eyes>

Answer 5

radicals are to exponents as division is to multiplication.

Answer 6

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)

Answer 7

Or even powers that is

Answer 8

so I don't understand what the lines represent on the sides of the answer?

Answer 9

Absolute value sign.

Answer 10

so the 4's basically cancel eachother out?

Answer 11

xactely

Answer 12

Yes.

Answer 13

If you have the same power as you have index on your radical it cancels out the exponent.

Answer 14

ok I think I understand. at least better. But what are the lines on each side for?

Answer 15

It's a nit picky detail.

Answer 16

| | is the absolute value operator.