SOLUTION: What is the simplified/expanded form of 16 to the -2/3 power? I know that if it was a non-negative exponent, the answer would just be cube root of (16²). But since the negative si

Algebra ->  Exponents -> SOLUTION: What is the simplified/expanded form of 16 to the -2/3 power? I know that if it was a non-negative exponent, the answer would just be cube root of (16²). But since the negative si      Log On


   

Question 1194006: What is the simplified/expanded form of 16 to the -2/3 power? I know that if it was a non-negative exponent, the answer would just be cube root of (16²). But since the negative sign means it will be inversed (meaning become a fraction), what is the numerator and what is the denominator?
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
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What is the simplified/expanded form of 16 to the -2/3 power?
I know that if it was a non-negative exponent,
the answer would just be cube root of (16²).
But since the negative sign means it will be inversed (meaning become a fraction),
what is the numerator and what is the denominator?
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As you know,  16^(2/3)  = root%283%2C16%5E2%29 = root%283%2C256%29.


The sign minus, " - " in the degree index,  16^(-2/3)  leads this number to the denominator, so

    16^(-2/3) = 1%2Froot%283%2C256%29.



If you want, you may calculate it using your calculator, or you may transform it further 

    16^(-2/3) = 1%2Froot%283%2C256%29 = 1%2Froot%283%2C2%5E8%29 = 1%2F%284%2Aroot%283%2C4%29%29


and then apply your calculator to this formula.