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Understanding the Properties of Exponents and Power Functions

In today's lesson, we will review the fundamental properties of exponents, deepening your understanding of the rules you may have previously encountered. Open your textbooks to page 245 and complete Investigation Steps 1-7 independently. Keep the Properties of Exponents Hand-Out in your notes. We will add more properties to our list and explore examples, including solving equations using common base properties. Homework includes problems from the 5.2 Worksheet. Let’s engage and learn together!

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Understanding the Properties of Exponents and Power Functions

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  1. Warm up • Today we will review the properties of exponents. • You may have learned this before, but hopefully today you will have a better understanding as to why the rules are what they are. • Open your textbooks to page 245. • Do the “Investigation” Steps 1-7. • Start by working alone. You will have a chance to work with a partner soon.

  2. Properties of Exponents and Power Functions

  3. Hand-Out • Keep this sheet in your notes! Little Fuckers! I love all you bitches. Now learn this shit and shut the FUCK UP!!! K-NEXT SLIDE!

  4. We need to add two more properties to the list… • You can write these on the back of your hand-out, or in the margins. Example of Common base property:

  5. Example 1: Use the properties to solve an equation. Solve:

  6. Example 1: solution • Original • Because • Power to a power property • Note: in problems like these, where x is the exponent and we are solving for x, we want to try and get a common base. This is an important step. • 3x = 2 Common base property • Divide.

  7. Example 2 • Rewrite as a fraction with no exponents:

  8. Example 2 Solution • Original • Negative Exponent

  9. Power Function • We know that an exponential function has the variable in the exponent. • A power function has a variable in the base. • General Equation for a power function:

  10. You have seen power functions before… • What is a common power function that you have seen?

  11. Power Rules • Remember: • What would equal?

  12. Example solving Power Functions • Solve for x:

  13. Solution • Original • Raise both sides to the power of 1/3 • 18.80 Simplify • x= 1.57 Divide by 12.

  14. Homework • 5.2 Worksheet: 1 a-g, 2 a-g, 3 a-c, 4 a-d.

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