Algebra

Please Simplify:

(root5 a^7/2)^4 a^3/a^8

So confused, I tried figuring this out but need some help tracing the steps. I would appreciate some feedback! Thanks!

asked by Carmin
  1. I have assumed that the fraction 7/2 is enclosed in parentheses, as follows:

    (sqrt(5)*a(7/2))4 a3/a8

    Since the bases of the exponents are "a" or 5, you only have to apply the following rules of exponents to get your answer of 25a9.

    1. sqrt(5) = 51/2
    2. distributive law:
    (ab)x = ax bx
    3. addition of exponents of same base
    ax ay = ax+y
    4. multiplication of exponents
    (ax )y = axy

    So:
    (sqrt(5)*a(7/2))4 a3/a8
    =(sqrt(5)4*(a(7/2))4) a3-8
    =25 a14 a-5
    =25 a9


    posted by MathMate
  2. WOW Thanks for the reply, but I still do not get how we get 25a^9. Can you please further explain. Thanks!

    posted by Carmin
  3. I get 25a^9/16? How can this be? Please help, still confused, thanks!

    posted by Carmin
  4. If you show your steps, it may help me spot where it has gone wrong.

    posted by MathMate
  5. ...
    =(sqrt(5)4*(a(7/2))4) a3-8
    =5(1/2)*4*a(7/2)*4*a3-8
    =25 a14 a-5
    =25 a9

    the denominator 2 in the fraction (7/2) is an exponent and not a simple number. This is probably from where you got the 16.

    posted by MathMate

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