CP Algebra I Homework: ________________________________________ 7.1 Zero and Negative Exponents Objectives: To simplify expressions with zero and negative exponents Warm Up: Complete without a calculator! 1. a) Fill in the chart with the value of the power in standard form. x 2x 5x 10 x 4 3 2 b) Look at the values that you used to replace the blanks. What pattern do you see as you go down each column? 2. Use the pattern you described in 1b to complete the table below. (If you use a calculator, leave your answers as a fraction) x 1 0 -1 -2 2x 5x 10 x The patterns that you found on the first page illustrate the definitions of zero and negative exponents. Zero as an Exponent Property: __________________________________________________________________________ Example 1): 50 = (-2)0 = (1.023)0 = Negative Exponent Property: ____________________________________________________________________________ Example 2): 6-4 = (-8)-1 = Quick Check: Simplifying Powers: What is the simplified form of each expression? 1) 9−2 2) (−3.6)0 3) 4−3 4) (−5)0 5) (−4)−2 Simplifying an Exponential Expression: An algebraic expression is in simplest form when powers with a variable base _____________________ _______________________________________________________________________________________________________________ Example 3): Simplify each expression (GOAL: Eliminate all negative exponents) a) 4𝑥 −3 𝑦 1 b) 𝑤−4 c) 7𝑠 −4 𝑡 2 d) 𝑛−5 𝑣2 e) 𝑠 0 𝑟 −3 Quick Check: Simplify Each Expression 1) 5𝑎3 𝑏 −2 1 2) 𝑥 −5 3) 5𝑏𝑐 −3 2 4) 𝑎−3 5) 𝑛−5 𝑚2 Evaluating an Exponential Expression: Always simplify the expression before substituting values in for the variables Example 4): Evaluate 3m 2t -2 for m = 2 and t = -3 (Hint: always use parenthesis!!) Example 5): Evaluate 𝑛−1 𝑤2 for n = - 2 and w = 5 Quick Check: Evaluate each expression for n = -2 and w = 5 a)n-3w0 n-2 b) 3 w w0 c) 4 n d) 1 nw-2 Using an Exponential Expression: Example 6) A population of marine bacteria doubles every hour under controlled laboratory conditions. The number of bacteria is modeled by the expression 1000 ∙ 2ℎ , where h is the number of hours after a scientist measures the population size. Evaluate the expression for h=0 and h= -3. What does each value of the expression represent in the situation? Quick Check: A population of insects triples every week. The number of insects is modeled by the expression 5400 ∙ 3𝑤 , where w is the number of weeks after the population was measured. Evaluate the expression for w= -2, w= 0, and w = 1. What does the value of the expression mean in the situation?