Simplify Expressions in Exponential or

Radical Form

4 3 2 1 0In 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 (91/2)(91/2) should be the same as 91/2+1/2 which is 91 or 9.

But, (3)(3) we also get 9.

Therefore, 91/2 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 10th root.

3. The numerator of the fraction is the power.1. A number with 2/3s power is the cube root of the number

squared.

Definition of bm/n

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

Practice #1 Evaluate 1001/2

The denominator is 2, take the square root of 100. The numerator is 1, take it to the 1st power. This means we are taking the square root of 100 to the 1st power. Which is the same as the square root of 100. 1001/2 = 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 3rd power. 163/2 = 64

Practice #3 Evaluate 1254/3

The denominator is 3, take the cube root of 125. This equals 5. The numerator is 4, take 5 to the 4th power. 1254/3 = 625

Write the radical using rational exponents.

Since a radical is involved, the exponent will be a fraction. Remember:◦ The denominator is the root.◦ The numerator is the power.

In 4 is the root = denominator. 1 is the power = numerator. = x¼

Practice #4

In 3 is the root = denominator. 2 is the power = numerator. = y2/3

Practice #5

In 4 is the root = denominator. 5 is the power = numerator. = 135/4

Apply More Exponent Properties Simplify: Same base, add the exponents. 2/3 + 3/8 = 25/24

Apply More Exponent Properties

Simplify:

Power to a Power = multiply the exponents (2/3)(3/4) = (6/12) = ½ y1/2