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Algebra

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I am trying to figure out how to evaluate 100^-3/2. I'm going by the example (64)^2/3=16. IN the example, 64^2/3 is changed into 64^1/3^2=4^2=16. But I don't get why out of all numbers it is changed into 4^2. I know 16 goes into 64 four times, but why is the answer 16 and what becomes of the 1/3? So how would this apply to 11^-3/2? Thanks for your help!

  • Algebra -

    First, you'd have to adhere to the rules of priority.
    The expression 642/3 is much clearer.
    The 2 in the exponent requires us to square the base, and the 3 in the denominator represents (1/3) means we need to take the cube root of the base.
    So whether you do ∛((64)²) or (∛64)³ will give the same answer, i.e. ∛(4096)=16 or (4)²=16. The 4 comes from the cube root of 64, or 641/3.

    For 11-3/2 it is the same procedure, by following the laws of exponents:
    xa+b = xa × xb
    xab = (xa)b
    x-a = 1/xa
    x1/a = ath root of x.

    Therefore
    11-3/2
    =1/113/2
    =1/∛(11³)
    =1/∛(1331)

  • Algebra-correction -

    11-3/2
    =1/113/2
    =1/√(11³)
    =1/√(1331)

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