Properties of Exponents and Power Functions

1. Properties of Exponentsand Power Functions Lesson 5.2

2. You will need to rewrite a mathematical expression in a different form to make the expression easier to understand or an equation easier to solve. Recall that If the exponent is a positive integer, you can write the expression in expanded form.

3. Properties of Exponents • Use expanded form to review and generalize the properties of exponents. • Write each product in expanded form, and then rewrite it in exponential form. • Generalize your results

4. Write the numerator and denominator of each quotient in expanded form. • Reduce by eliminating common factors, and then rewrite the factors that remain in exponential form. • Step 4 Generalize your results.

5. Write each quotient in expanded form, reduce, and rewrite in exponential form. • Rewrite each quotient using the property you discovered in the previous step. • Generalize your results:

6. Write several expressions in the form (an)m. Expand each expression, and then rewrite it in exponential form. • Generalize your results. • Write several expressions in the form (a·b)n. Don’t multiply a times b. Expand each expression, and then rewrite it in exponential form. • Generalize your results. • Show that a0 = 1, using the properties you have discovered. Write at least two exponential expressions to support your explanation.

8. Example A

10. Example B