I don't understand how to simply this:

$\displaystyle \sqrt[8]{256^2}$

The answer is 4 but I don't know how to work out the solution to get to 4.

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- Mar 26th 2010, 08:56 PMsoftwareguyHelp with how to simply using laws of exponents
I don't understand how to simply this:

$\displaystyle \sqrt[8]{256^2}$

The answer is 4 but I don't know how to work out the solution to get to 4. - Mar 26th 2010, 09:02 PMdwsmith
Calculator!

When you have a nth root of a term to the xth power, you can rewrite it in the form of 256^(x/n)=(nth root of 256)^x Now you can simplify the radical and then raise it to the x power.

Your n=8 and x=2 so the notation isn't confusing. - Mar 26th 2010, 09:03 PMDebsta
First of all you need to recognise that 256 = 2^8. (It is a really good idea to know all the powers of 2 up to 2^10 as they always crop up in problems. Also learn all the powers of 3 up to 3^5. It makes life with indices so much easier.

Replace 256 with 2^8. Replace the 8th root symbol with ^(1/8) so you have ((2^8)^2)(1/8).

Then use your index law that says (a^m)^n = a^mn and you will have your answer!!

DON'T TOUCH YOUR CALCULATOR!! - Mar 26th 2010, 09:04 PMumamaheswari
(256^2)^1/8

= 256^2*1/8

= 256^1/4

= 4^4*1/4

= 4.

note: ^ means 256 power 2

8th root is to the power 1/8 - Mar 27th 2010, 03:12 AMHallsofIvy