Math people can you check if i got these right!

Discussion in 'Community Discussion' started by waloshin, Jun 2, 2009.

  1. waloshin macrumors 68040

    waloshin

    Joined:
    Oct 9, 2008
    #1
    1) Express each of the following as a power of 2 and then simplify.

    A) (cubed root √4)^6 = (4) ^6/4 = (2^2) 6/4 = 2^12/4 = 2^3

    B) (1/64)^5/6 = (1/2^6)^5/6 = (2 ^-6)^5 = 26^-30 = 1/2^30

    2) Simplify the following radicals completely.

    A) 4th root √32 = 4th root 2√2

    B) 4th root √ 81x^8 z^6
    _______________
    w^12

    = 3x^2 z^4 √x^2
    ________________
    w^12
     
  2. Doctor Q Administrator

    Doctor Q

    Staff Member

    Joined:
    Sep 19, 2002
    Location:
    Los Angeles
    #2
    It's a bit hard to read the notation in a text post, but in general the steps you want to do are as follows:
    • Change roots to exponential form, i.e., change √x to x^(1/2), change cube root of x to x^(1/3), change fourth root of x to x^(1/4), etc.
    • If the problem involves raising 4 to a power, change the 4 to 2^2. If it involves raising 8 to a power, change the 8 to 2^3. And so on for 16, 32, 64, ....
    • Repeatedly use the rule that (x^n)^m = x^(nm), to combine exponents.
    Example:
    (Cube root of 32)^4 = (32^(1/3))^4 = ((2^5)^(1/3))^4 = 2^(5 x 1/3 x 4) = 2^(20/3)​
    Does that help you solve the problems in your assignment?
     

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