### Concept (1)

A negative coefficient of a term with a rational exponent can mean that we either (1) apply the rational exponent and then take the opposite of the result, or (2) the rational exponent applies to a negative term. In case 2 of rational exponents with negative coefficients, the answer will be not real if the denominator of the exponent is even. If the root is odd, the answer will be a negative number.

### Sample Problems (5)

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Simplify:

-253⁄2
###### Problem 1
How to evaluate a rational exponent with a negative coefficient.

Simplify:

(-27)5⁄3
###### Problem 2
How to evaluate a rational exponent with an odd root (an odd power) of a negative number.

Simplify:

(-125)
###### Problem 3
How to evaluate a rational exponent with an odd root and even power of a negative number.
###### Problem 4
Simplifying negative numbers raised to rational exponents.
###### Problem 5
Simplifying negative terms with multiple variables raised to rational exponents.