Main Idea and New Vocabulary NGSSS Key Concept
Main Idea and New Vocabulary NGSSS 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 7: Simplify Expressions Five-Minute Check
• Simplify real number expressions by multiplying and dividing monomials. • monomial
MA. 8. A. 6. 3 Simplify real number expressions using the laws of exponents. MA. 8. A. 6. 4 Perform operations on real numbers (including integer exponents, radicals, percents, scientific notation, absolute value, rational numbers, and irrational numbers) using multi-step and real world problems.
Multiply Powers Simplify 76 • 7. Express using exponents. 76 • 7 = 7 6 • 7 1 7 = 71 = 76 + 1 The common base is 7. = 77 Add the exponents.
Multiply Powers Check 76 · 7 = (7 · 7 7 · 7) · 7 =7· 7· 7 = 77 Answer: 77
Simplify 8 • 85. Express using exponents. A. 84 B. 85 C. 86 D. 88
Multiply Powers Simplify r 4 • r 6. Express using exponents. r 4 • r 6 = r 4 + 6 = r 10 Answer: r 10 The common base is r. Add the exponents.
Simplify t 9 • t 2. Express using exponents. A. t 4. 5 B. t 7 C. t 11 D. t 18
Multiply Powers Simplify – 7 x 2 • 11 x 4. Express using exponents. – 7 x 2 • 11 x 4 = (– 7 • 11)(x 2 • x 4) Commutative and Associative Properties = (– 77)(x 2 + 4) The common base is x. = – 77 x 6 Add the exponents. Answer: – 77 x 6
Simplify 4 n 6(– 2 n 5). Express using exponents. A. – 8 n 30 B. – 8 n 11 C. 8 n 30 D. 8 n
Divide Powers Simplify . Express using exponents. = 612 – 2 The common base is 6. = 610 Simply. Answer: 610
Simplify A. 82 B. 85 C. 815 D. 8– 5 . Express using exponents.
Divide Powers Simplify . Express using exponents. = a 14 – 8 The common base is a. = a 6 Simply. Answer: a 6
Simplify A. h 4 B. h 14 C. h 15 D. h 20 . Express using exponents.
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.
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
Simplify Expressions Simplify Group by common base. = 2 1 • 52 • 91 Subtract the exponents. = 2 • 25 • 9 52 = 25 = 450 Simplify. Answer: 450
Simplify A. 144 B. 1, 152 C. 1, 536 D. 9, 116 . Express using exponents.
Simplify 48 • 43. Express using exponents. A. 424 B. 411 C. 45 D. 4– 5
Simplify (– 3 x 6 yz 2)(– 2 xy 3). Express using exponents. A. – 6 x 7 y 4 z 2 B. 6 x 6 y 4 z 2 C. 6 x 6 y 4 z D. 6 x 7 y 4 z 2
Simplify A. 95 B. 9– 19 C. 919 D. 984 . Express using exponents.
Simplify A. a 15 b 30 B. a 8 b 13 C. a 2 b 10 D. a 2 b 7 . Express using exponents.
The population of Bangkok was 55 in 1620. By 1990, it increased 54 times. What was Bangkok’s population in 1990? A. 1, 953, 125 B. 6, 875 C. 555, 555 D. 390, 625
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