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Exponents • Two or more numbers that are multiplied together to form a product are called factors. • When the same factor is used, you may use an exponent to simplify the notation. The dots indicate multiplication. The exponent tells how many times the base is repeated. 16 = 2 2 2 2 = Common factors The base is the common factor. 4 2 • Numbers expressed using exponents are called powers. Powers Words 2 5 Five to the second power OR Five squared 3 4 Four to the third power OR Four cubed 4 2 Two to the fourth power Write each power as a product of the same factor. 142 14 × 14 54 5 5 5 5 75 7×7×7×7×7 Write each product in exponential form. 11 11 11 11³ 3 × 3 × 3 × 3 × 3 ×3 36 15 15 8 8 15² 8² 7×7×7×3×3 73 × 32 Evaluate each expression. Find the standard form. 3 squared 32 3×3 9 42 × 33 4×4×3×3×3 16 × 27 432 Evaluate each expression. Find the standard form. ten to the fifth power 105 10 10 10 10 10 100,000 three to the fourth power 34 3×3×3×3 9 × 9 81 Exponent Form Factor Form Standard Form 25 2x2x2x2x2 32 72 7x7 49 43 4x4x4 64 104 10 x 10 x 10 x 10 10,000 53 5x5x5 125 Exponents tell how many times a number, called a BASE, is used as a factor. 6² = 6 x 6 In 6 x 6, 6 is used as a factor twice. When you compute 6 x 6 or 6², you are finding the SQUARE of 6. 6 6 Find the squares of the following numbers: 1) 8 = 2 2 2) 12 = 3) 2 9 = 2 4) 10 = 64 144 81 100 (8x8) ( 12 x 12 ) (9x9) ( 10 x 10 ) Numbers like 36, 49, and 625 are called PERFECT SQUARES, because they are the squares of whole numbers. 6 6 6² = 36 If 6 is the number you would square to find 36, then 6 is the square root of 36. √36 = 6 What number would you square or is the square root of 9? 3 9 3 A radical sign ( √ ) is placed over a number when the square root is requested. What number would you square or is the square root of the following numbers: 1) √ 81 = 9 2) √ 121 = 11 (9x9) ( 11 x 11 ) 3) √ 49 = 7 (7x7) 4) √ 196 =14 ( 14 x 14 ) When given multiple choice answers to choose from for squares and square roots, first state the answer to the question, then match your answer with a multiple choice answer that represents the same. 1) Which of the following best represents √ 81 ? 81 81 9 18 9 2 9 9 2) Which if the following represents 3² ? 2 6 5 6 3 15 3 9 9 9 Which of the following best represents 6 √36 ? 1) 216 2) 12 3) 6 4) 36 6 6 6 Which of the following best represents 16 4² ? 6 16 1) 2) 3) 4) 4 16 4 4 Construct a Square Root Chart with your partner showing the numbers that 1-15 are the square roots of! Example √1 Square Root 1 √4 2 √9 3 √ 16 4 √ 25 5 YOUR ASSIGNMENT • Square and Square Roots WS YOUR ASSIGNMENT ---• Pg 32 #12-32 evens, • Pg 36 #10-30 evens