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Understanding Integer Exponents: Negative and Zero Powers

In this lesson, students will learn to read and say simplified exponents while mastering the simplification of expressions involving zero and integer exponents. Key concepts include understanding what a negative exponent represents and its applications in real-world scenarios. Students will explore how any nonzero number raised to the zero power equals 1 and that a nonzero number with a negative exponent translates to 1 divided by that number raised to the positive exponent. Engaging examples will help solidify these foundational concepts in algebra.

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Understanding Integer Exponents: Negative and Zero Powers

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  1. Algebra 7.1 Integer Exponents

  2. Learning Targets Language Goal • Students should be able to read and say simplified exponents. Math Goal • Students should be able to simplify expressions containing zero and integer exponents. Essential Question • What is a number to the negative power and where would you see it in the world around you?

  3. Warm-up

  4. Review Vocabulary • Who can remember what we call this number? • What is the 4? • What is the 5?

  5. Review Vocabulary • Base: The number in a power that is used as a factor. The 4 in our example. • Exponent: The number that indicates how many times the base is used as a factor.

  6. Exploration • What does it mean for an exponent to be negative or 0? • Example: • Hint: Use the table to look for a pattern to figure it out! 1

  7. Zero Exponent • Any nonzero number raised to the zero power is 1. =1 =1

  8. Negative Exponent • Negative Exponent-A nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the positive exponent.

  9. Chart Zero exponent- any nonzero # raised to the zero power is 1 Negative Exponent-A nonzero # raised to a negative exponent is equal to 1 divided by that # raised to the positive exponent.

  10. Example 1: Word Problems A. The diameter for the Model A Ford piston could vary by at most inch. Simplify this expression.

  11. Example 1: Word Problems B. One cup is gallons. Simplify this expression.

  12. Example 1: Word Problems C. A sand fly may have a wingspan up to meters. Simplify this expression.

  13. Example 2: Zero and Negative Exponents Simplify A. B. C.

  14. Example 2: Zero and Negative Exponents Simplify D. E.

  15. Example 3: Evaluating Expressions with Zero and negative Exponents. Evaluate each expression for the given value(s) of the variable(s). A. for x = 2 B.

  16. Example 3: Evaluating Expressions with Zero and negative Exponents. Evaluate each expression for the given value(s) of the variable(s). C. for p = 4 D. for a= -2 and b=6

  17. If you have an expression with a negative exponent in the denominator, it is equivalent to the same base with the opposite (positive) exponent in the numerator. • An expression is not simplified until this occurs.

  18. Example 4: Simplifying Expressions with Zero and Negative Exponents Simplify A. B. C.

  19. Example 4: Simplifying Expressions with Zero and Negative Exponents Simplify D. E. F.

  20. 7.1 Review WS

  21. 7.1 Review WS

  22. Lesson Quiz

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