University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

8

Pages:

2
Author:

anon

Power and Exponent Laws - A power is a product of identical factors and consists of two parts: a base and an exponent. 4←𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 𝐵𝑎𝑠𝑒 → 3 4 Exponential Form: 3 Expanded Form: 3 × 3 × 3 × 3 Evaluated: 81 Example 1: Write in expanded form, then evaluate: 4 4 a) (− 3) b) -3 = (− 3)(− 3)(− 3)(− 3 =-(3 × 3 × 3 × 3) =+ 81 =-81 3 3 4 2 3 3 3 2 2 2 3×3×3×3 2×2×2×2 81 16 ( ) =( )( )( )( ) c) (− 3) = (− 3)(− 3)(− 3) =− 27 d) = = = 3 2 Use the following table to develop the exponent laws. 2 Product 4 Expanded form 3×3×3×3×3×3 3 4 1 6×6×6×6×6 6 5 3 𝑘×𝑘×𝑘×𝑘×𝑘×𝑘×𝑘×𝑘 𝑘 𝑚 𝑛 (𝑥 + 𝑥 +...+ 𝑥) × (𝑥 + 𝑥 +...+ 𝑥) 𝑥 3 ×3 6 ×6 𝑘 ×𝑘 𝑥 ×𝑥 2 4 Single Power 6 5 8 𝑚+𝑛 6 -How are 3 × 3 and 3 related? -We are rewriting the base and adding the exponents 𝑚 𝑛 𝑚+𝑛 Product Rule: 𝑥 × 𝑥 = 𝑥 When multiplying the powers with the same base, add the exponents. Would the rule apply if the base was a rational number? Yes, it would. Ex: 𝑎 𝑚 𝑏 ( ) + 𝑎 𝑛 𝑏 𝑎 (𝑚+𝑛) ,𝑏 𝑏 ( ) =( ) ≠0 Complete the following table. Quotient 5 3 4 1 8 5 𝑚 𝑛 Expanded Form 5×5×5×5×5 5×5×5 7×7×7×7 7 𝑝×𝑝×𝑝×𝑝×𝑝×𝑝×𝑝×𝑝 𝑝×𝑝×𝑝×𝑝×𝑝 (𝑥×𝑥…×𝑥)←𝑚 (𝑥×𝑥…×𝑥)←𝑛 5 ÷5 7 ÷7 𝑝 ÷𝑝 𝑥 ÷𝑥 5 3 Single Power 2 25 = 5 3 7 3 𝑝 𝑚−𝑛 𝑥 2 Note: 5 ÷ 5 = 5 𝑚 𝑛 𝑚−𝑛 Quotient Rule: 𝑥 ÷ 𝑥 = 𝑥 When dividing powers with the same base, rewrite the base and subtract the exponents