## mathtard 3 years ago Find the following assuming that a can represent any real number $\sqrt[4]{(5a)}^{4}$

1. gandalfwiz

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

2. mathtard

so why would it be 5a?

3. polpak

it's actually |5a|

4. gandalfwiz

<rolls eyes>

5. polpak

radicals are to exponents as division is to multiplication.

6. polpak

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)

7. polpak

Or even powers that is

8. mathtard

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

9. polpak

Absolute value sign.

10. mathtard

so the 4's basically cancel eachother out?

11. gandalfwiz

xactely

12. polpak

Yes.

13. polpak

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

14. mathtard

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

15. polpak

It's a nit picky detail.

16. polpak

| | is the absolute value operator.