Main Idea and New Vocabulary Key Concept: Product of Powers Example 1: Multiply Powers Example 2: Multiply Powers Example 3: Multiply Powers Key Concept: Quotient of Powers Example 4: Divide Powers Example 5: Divide Powers Example 6: Real-World Example Example 7: Simplify Expressions Lesson Menu
Simplify real number expressions by multiplying and dividing monomials. Main Idea/Vocabulary
Key Concept
Simplify 76 • 7. Express using exponents. Multiply Powers Simplify 76 • 7. Express using exponents. 76 • 7 = 76 • 71 7 = 71 = 76 + 1 The common base is 7. = 77 Add the exponents. Example 1
Multiply Powers Check 76 · 7 = (7 · 7 · 7 7 · 7 · 7) · 7 = 7 · 7 · 7 7 · 7 · 7 · 7 = 77 Answer: 77 Example 1
Simplify 8 • 85. Express using exponents. A. 84 B. 85 C. 86 D. 88 Example 1 CYP
Simplify r4 • r6. Express using exponents. Multiply Powers Simplify r4 • r6. Express using exponents. r4 • r6 = r4 + 6 The common base is r. = r10 Add the exponents. Answer: r10 Example 2
Simplify t9 • t2. Express using exponents. A. t4.5 B. t7 C. t11 D. t18 Example 2 CYP
Simplify –7x2 • 11x4. Express using exponents. Multiply Powers Simplify –7x2 • 11x4. Express using exponents. –7x2 • 11x4 = (–7 • 11)(x2 • x4) Commutative and Associative Properties = (–77)(x2 + 4) The common base is x. = –77x6 Add the exponents. Answer: –77x6 Example 3
Simplify 4n6(–2n 5). Express using exponents. A. –8n30 B. –8n11 C. 8n30 D. 8n Example 3 CYP
Key Concept 4
Simplify . Express using exponents. Divide Powers Simplify . Express using exponents. = 612 – 2 The common base is 6. = 610 Simply. Answer: 610 Example 4
Simplify . Express using exponents. A. 82 B. 85 C. 815 D. 8–5 Example 4 CYP
Simplify . Express using exponents. Divide Powers Simplify . Express using exponents. = a14 – 8 The common base is a. = a6 Simply. Answer: a6 Example 5
Simplify . Express using exponents. A. h4 B. h14 C. h15 D. h20 Example 5 CYP
= 106 – 1 or 105 Quotient of Powers MEASUREMENT One centimeter is equal to 10 millimeters, and one kilometer is equal to 106 millimeters. How many centimeters are in one kilometer? 10 = 101 = 106 – 1 or 105 Quotient of Powers Answer: There are 105 centimeters in one kilometer. Example 6
MEASUREMENT One metric ton is equal to 106 grams and one hectogram is equal to 102 grams. How many times greater is a metric ton than a hectogram? A. 103 times greater B. 104 times greater C. 108 times greater D. 1012 times greater Example 6 CYP
= 21 • 52 • 91 Subtract the exponents. = 2 • 25 • 9 52 = 25 Simplify Expressions Simplify Group by common base. = 21 • 52 • 91 Subtract the exponents. = 2 • 25 • 9 52 = 25 = 450 Simplify. Answer: 450 Example 7
Simplify . Express using exponents. A. 144 B. 1,152 C. 1,536 D. 9,116 Example 7 CYP