## Tutoring on Performing Operations with Rational Exponents

Learning Objectives:

#### Understand to Perform Operations with Rational Functions.

Math Tutoring on Performing Operations with Rational Exponents

Exponent’s rules and properties are:

Product rules:       a ᵑ · b ᵑ = (a · b) ᵑ

Quotient rules:      a ᵑ / a ᵐ = a ᵑᵐ,     a ᵑ / b ᵑ = (a / b) ᵑ

Power rules:             (bᵑ)ᵐ = bᵑ

Other properties:       a¹ = a,  a° = 1

The above rules are valid for all real numbers a and b and rational numbers n and m, provided that all indicated powers are real and no denominator is zero. We see that, if the index is odd, then the radicand can be negative.  But if the index is even, the radicand may not be negative.  There is no such real number, for example, as rational exponents. When variable expressions involve even roots, we must be careful with signs. According to the power of a power rule:

and ,

i.e. the denominator of a fractional exponent is equal to the index of the radical.

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Hook Questions:

1. How do you write a radical expression?

2. What is a fractional exponent?

3. What is a radical form?

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