# Help with how to simply using laws of exponents

• March 26th 2010, 08:56 PM
softwareguy
Help with how to simply using laws of exponents
I don't understand how to simply this:

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

The answer is 4 but I don't know how to work out the solution to get to 4.
• March 26th 2010, 09:02 PM
dwsmith
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.
• March 26th 2010, 09:03 PM
Debsta
Quote:

Originally Posted by softwareguy
I don't understand how to simply this:

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

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

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).

• March 26th 2010, 09:04 PM
umamaheswari
(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
• March 27th 2010, 03:12 AM
HallsofIvy
Quote:

Originally Posted by umamaheswari
(256^2)^1/8
= 256^2*1/8

Caution! This is 256^(2*1/8) not (256^2)*(1/8).

Quote:

= 256^1/4
= 4^4*1/4
= 4.
note: ^ means 256 power 2
8th root is to the power 1/8