Exponents Notes

**Intro to Exponents Notes** **Math 9** **3.1 Exponents (D1)** **Introduction to Exponents** **Terminology:** Given 2^4 and -5^3 **Base:** the number being multiplied by itself (the number or variable that has an exponent attached to it) -5^3 = -1(5)^3 *The base is actually 5, not -5* **Exponent:** the number of times you multiply the base (the little raised number or variable) **Power:** an expression with a base and an exponent. **Example 1: Complete the chart** | Word Form | Repeated Multiplication | Exponential Form | Evaluate | |---|---|---|---| | Four cubed | 4 x 4 x 4 | 4^3 | 64 | | Negative two squared | (-2) x (-2) | (-2)^2 | 4 | | Fifth power of four | 4 x 4 x 4 x 4 x 4 | 4^5 | 1024 | | Negative five cubed | (-5) x (-5) x (-5) | (-5)^3 | -125 | | Ten to the exponent four | 10 x 10 x 10 x 10 | 10^4 | 10000 | **3 ways to write and evaluate powers** | Exponential Form | Repeated Multiplication | Standard Form | |---|---|---| | 2^5 | 2 x 2 x 2 x 2 x 2 | 32 | | 5^3 | 5 x 5 x 5 | 125 | **Example 2:** State the base and the exponent, write as a repeated multiplication and then evaluate. a) 5^3 **Math 9** **3.1 Exponents (D1)** ii) (-2)^3 (-2)(-2)(-2) = -8 iii) -2^3 -(2)(2)(2) = -8 iv) (-1/2)^3 (-1/2)(-1/2)(-1/2) = -1/8 v) -5^3 -(5)(5)(5) = -125 **Example 3: Are (-2)^3 and -2^3 equal?** (-2)^3 = (-2)(-2)(-2) = -8 -2^3 = -(2)(2)(2) = -8 No! **Investigate: What is the difference between 4^3 and 3 x 4? (Hint: repeated multiplication vs repeated addition)** 4^3 = 4 x 4 x 4 = 64 3 x 4 = 12 **Example 4: Write in Exponential Form** i) (6)(6)(6)(-4)(-4)(-4)(6)(6)(6)(-4) (6)^3(-4)^4 ii) (6)(6)(6)(-4)(-4)(-4)(6)(6)(6)(-4) (6)^3(-4)^4 **Math 9** **3.1 Exponents (D1)** **Example 5: Evaluate Each Power** 1. 4^2 (4)(4) = 16 2. -3^3 (-1)(3)(3)(3) = -27 3. (-4)^3 (-4)(-4)(-4) = -64 4. (-5)^3 (-5)(-5)(-5) = -125