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Zero and Negative Exponents: Expressions, Evaluation, and Real-World Applications

Learn how to write and evaluate expressions using positive and negative exponents, with examples and real-world applications. Understand the concept of negative exponents and simplify expressions involving negative exponents.

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Zero and Negative Exponents: Expressions, Evaluation, and Real-World Applications

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  1. Lesson Menu Main Idea Key Concept: Zero and Negative Exponents Example 1: Write Expressions using Positive Exponents Example 2: Write Expressions using Positive Exponents Example 3: Evaluate Expressions with Negative Exponents Example 4: Evaluate Expressions with Negative Exponents Example 5: Write Expressions using Negative Exponents Example 6: Write Expressions using Negative Exponents Example 7: Real-World Example: Use Negative Exponents Example 8: Multiply and Divide with Negative Exponents Example 9: Multiply and Divide with Negative Exponents

  2. Write and evaluate expressions using negative exponents. Main Idea/Vocabulary

  3. Key Concept

  4. Answer: Write Expressions using Positive Exponents Write 4–4 using a positive exponent. Definition of negative exponent Example 1

  5. A.–57 B.57 C. D. Write 5–7 using a positive exponent. Example 1 CYP

  6. Answer: Write Expressions using Positive Exponents Write c–7 using a positive exponent. Definition of negative exponent Example 2

  7. A.r8 B.–r8 C. D. Write r–8 using a positive exponent. Example 2 CYP

  8. Answer: Evaluate Expressions with Negative Exponents Evaluate 5–2. Definition of negative exponent 55 = 5 • 5 or 25 Example 3

  9. A.–20 B. C. D. Evaluate 4–5. Example 3 CYP

  10. Answer: Evaluate Expressions with Negative Exponents Evaluate (–8)–2. Definition of negative exponent (–8)2 = (–8)(–8) or 64 Example 4

  11. A.–125 B. C. D.125 Evaluate (–5)–3. Example 4 CYP

  12. Write as an expression using a negative exponent. Write Expressions using Negative Exponents 9 = 32 = 3–2Definition of negative exponent Answer: 3–2 Example 5

  13. Write as an expression using a negative exponent. A. B. C.7–2 D.72 Example 5 CYP

  14. Write as an expression using a negative exponent. Definition of negative exponent Write Expressions using Negative Exponents Answer: f –5 Example 6

  15. Write as an expression using a negative exponent. A.m–6 B.–m6 C. D. Example 6 CYP

  16. Use Negative Exponents SCIENCEA grain of salt weighs about 0.0001 gram.Write the decimal as a power of 10. Write the decimal as a fraction. 10,000 = 104 = 10–4Definition of negative exponent Answer: A grain of salt weighs about 10–4 gram. Example 7

  17. FISHA sea horse travels about 0.01 mile per hour. Write the decimal as a power of 10. A.103 B.102 C.10–2 D.10–3 Example 7 CYP

  18. Answer: Multiply and Divide with Negative Exponents Simplify a–5• a–3. Express using positive exponents. a–5• a–3 = a–5 + (–3)Product of Powers = a–8 Add the exponents. Definition of negative exponents Example 8

  19. A.x10 B.x2 C. D. Simplify x4• x–6. Express using positive exponents. Example 8 CYP

  20. Simplify . Express using positive exponents. Multiply and Divide with Negative Exponents Quotient of Powers = c2Subtract the exponents. Answer: c2 Example 9

  21. Simplify . Express using positive exponents. A.812 B.86 C. D. Example 9 CYP

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