What strategy did you use to solve for x? Minds On… Solve for 𝑥: 8𝑥 −6=−2 1 2 𝑥+9=7 4 3𝑥 =12 Using inverse operations What strategy did you use to solve for x?

Solving Equations Using Rational Exponents LG: I can rearrange and solve equations with rational exponents

Solving for a Base in a Power Inverse operations can be used to solve equations with exponents. Remember that a radical is the inverse of power Example 1: 𝑥 4 =16 x = 16 1 4 𝑥= 4 16 𝑥=2

Example 2: 𝑥 3 2 =27 x = 27 2 3 𝑥= 3 27 2 𝑥= 3 2 𝑥=9 Try This: 𝑥 3 = 125 64

TRY THIS. A lab technician starts with 1 salmonella bacterium TRY THIS! A lab technician starts with 1 salmonella bacterium. She uses the equation 𝑃= 2 3𝑡 to model the population, P, after t hours. Use the equation to determine when there will be 1000 bacteria in the population Trial and error or find a common base

Solve by Finding a Common Base Equality of Powers: If 𝑎 𝑚 = 𝑎 𝑛 , then 𝑚=𝑛 5 𝑥 = 5 6 2 𝑥 =32 7 3𝑥 −4 =49 3 5𝑥+8 = 27 𝑥 2 2(𝑥−5) = 4 3𝑥−1 9 𝑥+1 = 27 𝑥

Practice Questions Pg. 377 #10 Pg. 384 #1-7