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Note that a number to a negative exponent is not necessarily a negative number.
Fractional Exponents
In a fractional
exponent, the
numerator is the power to which the number should be taken and the denominator
is the root which should be taken. For example, 125 means "take
125 to the fourth power and take the cube root of the result" or "take the cube
root of 125 and then take the result to the fourth power." Order does not
matter when evaluating exponents--it is usually easier to take the root first,
and then take the power.
Since we cannot take the even root of a negative number, we cannot take a
negative number to a fractional power if the denominator of the exponent is
even.
A negative fractional exponent works just like an ordinary negative exponent.
First, we switch the numerator and the denominator of the base number,
and then we apply the positive exponent.