Simplify Expressions in Exponential or Radical Form

43210 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will construct, compare, and interpret linear and exponential function models and solve problems in context with each model. - Compare properties of 2 functions in different ways (algebraically, graphically, numerically in tables, verbal descriptions) - Describe whether a contextual situation has a linear pattern of change or an exponential pattern of change. Write an equation to model it. - Prove that linear functions change at the same rate over time. - Prove that exponential functions change by equal factors over time. - Describe growth or decay situations. - Use properties of exponents to simplify expressions. Students will construct, compare, and interpret linear function models and solve problems in context with the model. - Describe a situation where one quantity changes at a constant rate per unit interval as compared to another. Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal. Focus 8 Learning Goal – (HS.N-RN.A.1 & 2, HS.A-SSE.B.3, HS.A-CED.A.2, HS.F-IF.B.4, HS.F-IF.C.8 & 9, and HS.F-LE.A.1) = Students will construct, compare and interpret linear and exponential function models and solve problems in context with each model.

Review: When we multiply powers of the same base, the exponents are added together. So (9 1/2 )(9 1/2 ) should be the same as 9 1/2+1/2 which is 9 1 or 9. But, (3)(3) we also get 9. Therefore, 9 1/2 must equal 3!

A Few Rules… 1.You’re allowed to have exponents that are fractions! 2.The denominator of the fraction is the root. 1.A denominator of 2 means a square root. 2.A denominator of 3 means a cube root. 3.A denominator of 10 means a 10 th root. 3.The numerator of the fraction is the power. 1.A number with 2 / 3 s power is the cube root of the number squared.

Definition of b m/n For any nonzero real number b, and any integers m and n with n > 1,

Practice #1 Evaluate 100 1/2 The denominator is 2, take the square root of 100. The numerator is 1, take it to the 1 st power. This means we are taking the square root of 100 to the 1 st power. Which is the same as the square root of /2 = 10 Anything to the ½ power is just the square root of that number.

Practice #2 Evaluate 16 3/2 The denominator is 2, take the square root of 16. This equals 4. The numerator is 3, take 4 to the 3 rd power. 16 3/2 = 64

Practice #3 Evaluate 125 4/3 The denominator is 3, take the cube root of 125. This equals 5. The numerator is 4, take 5 to the 4 th power /3 = 625

Write the radical using rational exponents.

Practice #4

Practice #5

Apply More Exponent Properties

Simplify: Power to a Power = multiply the exponents ( 2 / 3 )( 3 / 4 ) = ( 6 / 12 ) = ½ y 1/2