In general, the rule of negative exponents says that for any number x that is raised to the power of a negative number, the power is moved to the denominator and made positive. For example, say you have

x^-2.

The negative exponent rule says that this is actually the same as,

(1/x^2).

The proof for this is as follows:

(1/x^2) = (x^0/x^2) = x^0-2 = x^-2.

The rule holds true whether you x is raised to the power of a whole number or a fraction. Say, for example, you have

x^-1/2.

The negative exponent rule remains the same, and you simply move this power to the denominator:

(x^-1/2) = (1/x^1/2)

Now, we can apply another rule to this number. The definition of (1/a^n) says that this number can be rewritten using radicals. So,

(1/x^1/2) = (1/`sqrt(x)` )

We can apply this same rule to real numbers. Say we have

(125^-1/3)

This is the same as

(1/125^1/3)

Which is the same thing as saying

(1/cuberoot 125)

The cube root of 125 is 5, so the final answer here would be

(1/5).

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