Main Idea NGSSS Key Concept Zero and Negative

Main Idea NGSSS 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 Five-Minute Check

• Write and evaluate expressions using negative exponents.

MA. 8. A. 6. 3 Simplify real number expressions using the laws of exponents.

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

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

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

Write r– 8 using a positive exponent. A. r 8 B. –r 8 C. D.

Evaluate Expressions with Negative Exponents Evaluate 5– 2. Definition of negative exponent 52 = 5 • 5 or 25 Answer:

Evaluate 4– 5. A. – 20 B. C. D.

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

Evaluate (– 5)– 3. A. – 125 B. C. D. 125

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

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

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

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

Use Negative Exponents SCIENCE A 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– 4 Definition of negative exponent Answer: A grain of salt weighs about 10– 4 gram.

FISH A 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

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 Answer:

Simplify x 4 • x– 6. Express using positive exponents. A. x 10 B. x 2 C. D.

Multiply and Divide with Negative Exponents Simplify . Express using positive exponents. Quotient of Powers = c 2 Answer: c 2 Subtract the exponents.

Simplify A. 812 B. 86 C. D. . Express using positive exponents.

Write 7– 6 using a positive exponent. A. – 76 B. 76 C. D.

Write (– 10)– 3 using a positive exponent. A. B. C. – 103 D. 103

Write x– 5 using a positive exponent. A. B. C. x 5 D. (–x)5

Simplify 6– 2 • 65. Express using positive exponents. A. 6– 3 B. 63 C. 6– 10 D. 610

Simplify A. 8– 15 B. 8– 2 C. 82 D. 815 . Express using positive exponents.

Simplify – 5 x 2 y – 2 • 3 x– 3 y 5. Express using positive exponents. A. – 15 xy 3 B. C. D.

Simplify A. ab B. C. D. . Express using positive exponents.

Which of the following correctly shows 11– 3, 111, 113, 110, and 11– 1 in order from least to greatest? A. 11– 1, 11– 3, 110, 111, 113 B. 110, 11– 3, 11– 1, 113 C. 113, 111, 110, 11– 1, 11– 3 D. 11– 3, 11– 1, 110, 111, 113