Fractional Exponents - Is the sign discarded?For example,16^(3/4)Is the accepted as both -8 and 8 or just 8?I ask this because on an AS maths mark scheme it says to condone -8Thanks

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humbast2 · Accepted Answer

There is a common missunderstanding of the function square-root, that often produce confusions when talking about fractional powers with an even denominator. First of all, note that the domain of   f  (  x  )  =      x   is the non-negative real numbers, and the possible values it takes are always positive. So, for instance,       4    =  2, or       9    =  3However, a different thing is to ask about the possible solutions of the equation       x    2    =  4, which are two different values:   x  =  2  =      4   and   x  =  −      4    =  −  2. Note that in the last equation the minus sign is outside of the square root, which indicates that the value of       4   is positive.Usually, when solving the equation       x    2    =  9 we say   x  =  ±      9    =  ±  3, but this does not mean that the square root of   9 is both positive and negative, but rather that there are two solutions of the equation, on if       9    and the other one is   −      9   (a completely different number).So, it is not that both   8 and   −  8 are equal to       16          3              /            4       (which would imply that   −  8  =  8, and this is absurd!). In this case we have:      16          3              /            4        =  (      16          1              /            2            )          3              /            2        =  (      16        )          3              /            2        =      4          3              /            2        =  (      4        )    3    =      2    3    =  8

Fractional Exponents - Is the sign discarded? For example, 16^(3/4) Is the accepted

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