Results 1 to 5 of 5

Math Help - Help with how to simply using laws of exponents

  1. #1
    Junior Member
    Joined
    Mar 2010
    Posts
    26

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    311
    Thanks
    2
    Quote Originally Posted by softwareguy View Post
    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).
    Then use your index law that says (a^m)^n = a^mn and you will have your answer!!

    DON'T TOUCH YOUR CALCULATOR!!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2010
    Posts
    2
    (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
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,790
    Thanks
    1531
    Quote Originally Posted by umamaheswari View Post
    (256^2)^1/8
    = 256^2*1/8
    Caution! This is 256^(2*1/8) not (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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Laws of Exponents
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: June 2nd 2011, 05:13 PM
  2. Laws of exponents
    Posted in the Algebra Forum
    Replies: 7
    Last Post: May 11th 2011, 02:19 AM
  3. Question on Laws of Exponents
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 25th 2011, 06:19 AM
  4. exponent laws and negative exponents
    Posted in the Algebra Forum
    Replies: 5
    Last Post: October 18th 2008, 02:03 PM
  5. Replies: 9
    Last Post: May 22nd 2008, 09:03 PM

Search Tags


/mathhelpforum @mathhelpforum