Learning Objectives:

__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 ᵑ****⁻****ᵐ, a ᵑ / b ᵑ = (a / b) ᵑ **

**Power rules: (bᵑ)ᵐ = bᵑ****⁻****ᵐ **

**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? *

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