Main Idea and New Vocabulary Key Concept Product

Main Idea and New Vocabulary Key Concept: Product of Powers Example 1: Multiply Powers Example 2: Multiply Monomials Example 3: Multiply Monomials Key Concept: Quotient of Powers Example 4: Divide Powers Example 5: Divide Powers Example 6: Real-World Example

• Multiply and divide monomials. • monomial

Multiply Powers Find 85 • 8. Express using exponents. 85 • 8 Answer: 86 = 8 5 81 8 = 81 = 85 + 1 is 8. The common base = 86 Add the exponents. Check 85 • 8 = (8 • 8 • 8) • 8 = 8 • 8 • 8 • 8 or 86

Find 44 • 42. Express using exponents. A. 42 B. 44 C. 46 D. 48

Multiply Monomials Find f 6 • f 3 = f 6+3 = f 9 Answer: f 9 The common base is f. Add the exponents.

Find g 2 • g 9. A. g 7 B. g 11 C. g 18 D. g 29

Multiply Monomials Find – 3 x 6 y 2 • 2 x 4 y 3. (– 3 x 6 y 2)(2 x 4 y 3) = (– 3 2)(x 6 x 4) (y 2 y 3) Use the Commutative and Associative Properties. = (– 6)(x 6 + 4) (y 2 + 3) The common bases are x and y. = – 6 x 10 y 5 Answer: – 6 x 10 y 5 Add the exponents.

Find – 1 x 3 • – 4 x 4 y. A. 4 x 7 y B. – 4 x 7 y C. 4 xy D. – 4 xy

Divide Powers Find The common base is 4. = 47 Answer: 47 Subtract the exponents.

Find A. 315 B. 38 C. 32 D. 3

Divide Powers Find . The common base is x. = x 2 Answer: x 2 Subtract the exponents.

Find A. y B. y 8 C. y 15 D. y 56

BACTERIA A scientist determines that Bacteria A multiply at a rate of 98 per second. Bacteria B were determined to multiply at a rate of 95 per second. Find how many times faster Bacteria A multiply than Bacteria B. The common base is 9. = 93 Subtract the exponents. Answer: So, Bacteria A multiply 93 or 729 times faster than Bacteria B.

PICTURES Alexi took 25 pictures on the class trip. Brittany took 24 pictures. Find how many more pictures Alexi took than Brittany. A. 2 times more B. 3 times more C. 22 times more D. 24 times more