MPM1D Exponents Ms. Kueh Some terms can be written as a power. Eg. “Two to the exponent six” or “Two to the six” or “Two to the power of 6” Power Form Expanded Form Standard Form 2 6 2 x 2 x 2 x 2 x 2 x 2 64 *Powers are short forms for multiplication. 1. Complete the following table. Expanded Form Power Form Standard Form a. (2) (2) (2) (2) (2) (2) b. c. yyyyyyyy d. (-3y) (-3y) (-3y) 2. Write the power in expanded form and then evaluate. Power Form Expanded Form Standard Form a. 3 2 b. 2 3 c. d. (-3) 3 3. What is the difference between 2 5 and 2(5)? 4. Evaluate each power. Exponent Base No Calculators

a) (- 5) 2 b) - 5 2 c) - (- 5) 2 d) 5 2 Multiplying Powers In this activity you will discover the shortcut for multiplying powers. b. Complete the following table. Question Answer in Expanded Form Answer in Power Form a ( 3 2 )( 3 4 ) ( 3 )( 3 )( 3 )( 3 )( 3 )( 3 ) b ( 2 ¿¿ 4 )( 2 3 ) ¿ c ( 5 ¿¿ 4 )( 5 2 ) ¿ d ( 2 3 ) 4 ( 2 3 ) 3 e ( − 2 ) 5 ( − 2 ) 2 c. Based on your answers in question 1, can you determine a shortcut for multiplying powers so that you don't have to write out every question in expanded form? When multiplying powers with the same bases, keep the __________ and ____________ the exponents. d. Use your shortcut to simplify the following. a. ( 5 3 )( 5 12 ) b. ( 2 23 )( 2 10 ) c. ( 7 ¿¿ 5 )( 7 13 ) ¿ d. ( 10 ¿¿ 6 )( 10 ) ¿ e. ( 4 ¿¿ 2 )( 4 9 ) ¿ f. ( 3 ) ¿ ) g. ( y 4 )( y 16 ) h. ( x ¿¿ 2 )( x 11 ) ¿ i. ( a )( a 105 )