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    Why is  \frac{1} {16}^{-1}= 16? I know that  a^{-m}= \frac{1} {a^{m}}

    I understand that a number can be turned into a fraction via this rule, but I don't understand why a fraction can become a whole number because of  ^{-1}.

    I can see that it is effectively the inverse function, but I don't understand exactly what is happening to the fraction to convert it back into a whole number.
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    (Original post by Illidan2)
    Why is  \frac{1} {16}^{-1}= 16? I know that  a^{-m}= \frac{1} {a^{m}}

    I understand that a number can be turned into a fraction via this rule, but I don't understand why a fraction can become a whole number because of  ^{-1}.

    I can see that it is effectively the inverse function, but I don't understand exactly what is happening to the fraction to convert it back into a whole number.
    If you divide 1 by a fraction then the fraction flips:

    \displaystyle \left(\frac{a}{b}\right)^{-1} = \frac{1}{ \left( \frac{a}{b} \right) } = 1 \div \frac{a}{b} = 1 \times \frac{b}{a} = \frac{b}{a}

    So in this case:

    \displaystyle \left(\frac{1}{16}\right)^{-1} = \frac{1}{ \left( \frac{1}{16} \right) } = \frac{16}{1}
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    Ahh, I see! Thank you again!
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    By having a negative indice, you are dividing something by 1/(the denominator of the indice), hence, if you have (1/16)^-1, you are basically doing (1/16) / (1/1). The rules of dividing fractions states that you must flip the first fraction (so it becomes 16/1) and then the divide sign becomes a multiply, so it's (16/1 * 1/1), which is just 16
 
 
 
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