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Mathematics 9 Unit: Powers and Roots Name: Date: Positive Exponents Define: Base, Exponent, Power, Repeated Multiplication (Factored) Form, Standard Form, Exponential Form, Variable, Coefficient Remember: When an integer, other than 0, can be written as a product of equal factors, we can write the integer as a power. Exponents are used as a short way to write repeated multiplication. Base 92 Power Exponent “Nine squared” or “Nine to the exponent two” Standard Form Repeated Multiplication Form Exponential Form 81 9×9 92 125 5×5×5 53 Mathematics 9 Unit: Powers and Roots Name: Date: Work with a partner for this activity and don’t forget to recycle your paper when done! Explore: When you repeatedly fold a piece of paper in half, the number of layers increases with the number of folds. Fold a standard piece of paper, and copy and complete the table. Number of Folds 1 2 3 4 5 6 Number of Layers (Repeated Multiplication, Standard, Exponential) 2 = 2 = 21 2 × 2 = 4 = 22 If you were to fold a piece of paper the following numbers of times, how many layers would you have? Express each answer in exponential form. a. 4 b. 8 c. 27 If 10 layers of paper are about 1 mm thick, how thick is a piece of paper after 10 folds? What is the maximum number of times you can fold a piece of paper? Mathematics 9 Unit: Powers and Roots Name: Date: Remember: If the base is given in brackets, do not get rid of the brackets!! Class Example: Write the following powers in repeated multiplication and standard form. Exponential Form Repeated Multiplication Form Standard Form 74 Exponent only applies to the number or variable directly underneath! 7×7×7×7 2401 2 2 2 × × 3 3 3 8 27 (-5)4 (-5) × (-5) × (-5) × (-5) 625 -54 -1 × 5 ×5 × 5 × 5 -625 2 3 3 Try On Your Own: Write the following powers in repeated multiplication and standard form. Exponential Form Repeated Multiplication Form Standard Form -23 (-2)3 -(-5)6 34 Apply the rules for multiplying integers: The sign of a product with an even number of negatives is positive. The sign of a product with an odd number of negatives is negative. Example: 2 (-3) = (-3)(-3) = 9 (-3)3 = (-3)(-3)(-3) = (-27) Even Positive Odd Negative