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Exploring Exponents: Understanding Functions and Financial Growth

This educational resource provides insights into simplifying expressions with exponents, answering questions about exponential growth in financial contexts, and understanding the fundamental rules of exponents. Students will learn how to evaluate expressions like (3^{3+2}) when (x=10) and formulate equations for exponentially growing investments, like calculating the future value of $500 that doubles yearly. The material covers essential exponent rules, including product, quotient, and zero exponent rules.

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Exploring Exponents: Understanding Functions and Financial Growth

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  1. I can simplify expressions with exponents. What is the value of 3x3+2 when x=10? You put $500 in an account that doubles every year. What is the equation for this situation? How much money would you have after 4 years? Warm Up (x=years y=money)

  2. Homework Questions

  3. What an Exponent Represents • An exponent tells how many times a number is multiplied by itself. 4 = 3  3  3 3 = 81 3

  4. How do you say this? three to the third power or three cubed Exponent 3 3 Base

  5. How do you say this? three to the 2ndpower Or three squared Exponent 3 2 Base

  6. Practice: Write in many different ways 1. 9  9 = 2. 8  8  8  8 = 4096 eight x 3. x  x  x  x  x =

  7. Exponent Rules

  8. Part 1 Product Rule: Multiply same base, add the exponents Example:

  9. Part 2 Quotient Rule: Divide same base, subtract the exponents Example:

  10. Part 3 Power Rule: Same base, multiply the exponents Example:

  11. Part 4 Expanded Power Rule: Apply outside exponent to all parts inside parenthesis Example:

  12. Part 5 Expanded Power Rule (cont): = Apply outside exponent to all parts inside parenthesis Example:

  13. Part 6 Zero Exponent Rule: Any base raised to 0 equals 1. Example:

  14. NOTES

  15. Negative Exponents • Negative exponents tell you how many times you should divide by a number • Negative exponents move the base to bottom of a fraction Note: the exponent becomes positive

  16. Negative Exponents

  17. Partners • Find a partner with a different letter • Compare and check each others answers

  18. Worksheet Complete any 10 problems

  19. What’s the difference? 1) 2)

  20. What’s the difference? 3) 4)

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