Law of Exponents for Multiplication Number Sense and Operations Grade 7

Think About It = 5 * 5 * 5 * 5 * 5 * 5 = 5 * 7 Multiplication is shorthand for repeated addition Exponential form is shorthand for repeated multiplication

Powers of 5s Product of 5Exponential Notation 55¹ 5 * 55² 5 * 5 * 55³ 5 * 5 * 5 * The Raised number is called an exponent. The exponent tells us how many times a number is multiplied by itself.

Examples 2 * 2 * 2 * 2 *2 * 2 = 9 * 9 * 9 * 9 * 9 = 3 * 3 * 3 * 3 =

Multiplying Exponents with the Same Base 6 * 6 = 6 1 * 6 1 = * (6 * 6) = 6 1 * 6 2 = 6 3 (6 * 6) * (6 * 6) = 6 2 * 6 2 = 6 4 (6 * 6) * (6 * 6 * 6) = 6 2 * 6 3 = 6 5

Addition Law of Exponents b m * b n = b m+n To Multiply two numbers with like bases, add exponents.

Addition Law of Exponents Arithmetic 7 3 * 7 6 = Algebra x 2 * x 4 = 7 (3+6) = 7 9 x (2+4) = x 6

Examples Simplify 8 3 * 8 6 = 9 5 * 9 -2 = Can 7 2 * x 6 be simplified?= 8 (3 +6) = (5-2) = x 6

Challenges Explain why -2 4 is negative and (-2) 4 is positive

Use a calculator Find the value of 15 2 and 8 6. To find the value of 15 2 Key in: 15 ^ 2 enter. Answer: 225 To find the value of 8 6 Key in: 8 ^ 6 enter. Answer:262,144 You can verify this by keying in 8 * 8 * 8* 8 * 8 * 8 enter

Write the solutions in exponent form, applying the addition law of exponents whenever possible, using the stacking counters y 2 * y 7 (xy) 2 * (xy) 2 a 6 * a -3 x 5 * x 8 x 2 * xx 3 * x 3 a 6 * a -3 z 7 * z 4 y 1 * y 3 z 5 * z 2 x 7 * x 1 x 4 * x 2

Closure What did you learn today? What questions do you still have about the topic? Complete the handout for homework.