How To Solve Negative Fraction Exponents?

Quick answer:

To figure out negative fractional exponents, simply move the number and the exponent to the denominator, make the exponent positive, and then turn the exponent into a radical.

Expert Answers

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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


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


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


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


This is the same as


Which is the same thing as saying

(1/cuberoot 125)

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


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