6.1.2 Powers and Exponents

Vocabulary Review Operation Words Algebra Addition The sum of a + b Subtraction The difference of a – b Multiplication The product of a x b a · b (a)(b) ab Division The quotient of a ÷ b a/b b a

Vocabulary Base – the repeated factor Power – a factor and exponent In the examples to the right, 5 is the base Product – multiplication answer 36 is a product of 6 x 6 6 x 6 is also a product, it’s just not solved yet Power – a factor and exponent Example: 5³ “5 to the third power” “5 to the power of three” “5 cubed” Exponent – the number of times to repeat a factor In the examples above, 3 is the exponent

Why squared? Why cubed? A factor to the power of 2 is called “squared” A factor to the power of 3 is called “cubed” A factor to the power of 4 is called “fourth power”…5 is “fifth power” and so on Here’s why… To find the area of a SQUARE, you multiply TWO sides To find the area of a CUBE, you multiply THREE sides 3 2 2 1 1

Write the product as a power 5 · 5 · 5 · 5 · 5 · 5 Because 5 is used as a factor six times, the exponent is 6 So, 5 · 5 · 5 · 5 · 5 · 5 = 5⁶ 5 is the base; 6 is the exponent 13 · 13 · 13 · 13 Because 13 is used as a factor four times, the exponent is 4 So, 13 · 13 · 13 · 13 = 13⁴ 13 is the base; 4 is the exponent

Your turn Write each of the products below as an exponent: 6 · 6 · 6 · 6 · 6 = 2 · 2 · 2 · 2 = 17 · 17 · 17 · 17 · 17 · 17 · 17 · 17 · 17 · 17 = 9 · 9 = 31 · 31 · 31 =

Finding the values of Powers Write the power as repeated multiplication 7² = 7 · 7 then simplify = 49 5³ = 5 · 5 · 5 = 125

Perfect squares The square of a whole number is a perfect square Here are a few perfect squares: 36 (6 · 6 or 6²) 25 (5 · 5 or 5²) 81 (9 · 9 or 9²) What is 16 a perfect square of? What is 100 a perfect square of? What is 121 a perfect square of?

Your Turn Find the value of the power 6³ = 3⁴ = 18² = Determine if the number is a perfect square 25 yes or no 2 yes or no 99 yes or no 49 yes or no

Homework Page 14 #2, 3, 4, 8, 10, 11, 14, 16, 17, 20, 21, 23, 24