1. Lesson 5.3 Products and Quotients of Powers

2. ( ) 3 b n = 1 · b · b · b · … · b n times Remember that the exponent n in the power b n counts the number of times that 1 is multiplied by the base b. So, Raising to the n th power can be viewed as an operator: ( ) n For example, when the exponential operator ( ) 3 is applied to the operand 2, the transform is 2= 8 = 1 · 2 · 2 · 2 multiply by 2 a total of 3 times Remember: If b  0, then b 0 = 1 and for all b, b 1 = 1 · b = b. 0 0 is not defined.

3. 7 3 · 7 2 = (7 · 7 · 7)(7 · 7) = 7 · 7 · 7 · 7 · 7 = 7 5 Simplifying a Product of Powers General rule: x m · x n = x m + n To multiply powers with the same base, add their exponents. Simplifying a Quotient of Powers To divide powers with the same base, subtract their exponents. 3 + 2 = 5 5 – 2 = 3 75727572 (7 · 7 · 7)(7 · 7) (7 · 7) = 7 · 7 · 7 · 7 · 77 · 77 · 7 · 7 · 7 · 77 · 7 = 7 · 7 · 7 = 7 3 = Cancel the multiplying and dividing by 7 · 7. General rule: x mx nx mx n = x m – n

4. 353353 35313531 = Examples: Replace each product or quotient by an equivalent power. 2 4 · 2 3 The bases are the same, so add the exponents. 2 4 · 2 3 = 2 4 + 3 = 2 7 Subtract the exponents. 9 4 · 9 0 Add the exponents. 9 4 · 9 0 = 9 4 + 0 = 9 4 Recall that 9 0 = 1, so multiplying by 9 0 is the same as multiplying by 1. 353353 35313531 == 3 5 – 1 = 3 4