## Tutoring on Exponents and Simplifying Expressions with Exponents

Learning Objectives:

#### Understand to Simplify Expressions with Exponents.

Exponents and Simplifying Expressions with Exponents

Exponential notation or exponential form is commonly found in algebraic terms, expressions and equations.  Exponents are used to shorten or condense repeated multiplication. Here is an example,  3 x 3 x 3 x 3 x 3 = 3 to the power of 5, i.e.35 the term 3 to the fifth is written using exponential notation. 3 is the base and 5 is the exponent. The exponent or power indicates the number of times that the factoror base is multiplied together. In general, for any natural number n, b to the nth power or b ᵑ means b times itself n times. So that will be n factors of b.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

Hook Questions

1.    What is the product property of exponents?

2.    Why do you subtract the exponents when dividing powers of the same base?

3.    What is a number to a negative power?

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