1. Warm Up! Write down the objective and homework in your agenda Lay out homework (Writing & Simplifying expressions wkst) Homework (Kuta Rational Exponents wkst)

2. Unit 1 Common Core Standards 8.EE.7 Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real- world and mathematical problems in two and three dimensions. 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Note: At this level, focus on linear and exponential functions. A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. Note: At this level, limit to formulas that are linear in the variable of interest, or to formulas involving squared or cubed variables.

3. Unit 1 Common Core Standards A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Note: At this level, focus on linear and exponential functions. A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A-SSE.1 Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. Note: At this level, limit to linear expressions, exponential expressions with integer exponents and quadratic expressions. G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. Note: Informal limit arguments are not the intent at this level. G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* Note: At this level, formulas for pyramids, cones and spheres will be given. G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

4. Unit 1 Common Core Standards N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (5 1/3)3 must equal 5. N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Note: At this level, focus on fractional exponents with a numerator of 1. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

5. Warm Up What is the difference between an expression and an equation? Give an example of each. What is the difference between solving an equation and simplifying and expression? Simplify -(3x + 5) - 4x + 3 Write & solve

6. Warm Up What is the difference between an expression and an equation? Give an example of each. Expression: no equal sign, Equation: equal sign Expression: 4x + 5 Equation: 23 + x = 9 What is the difference between solving an equation and simplifying and expression? Solving an equations means you have one final answer, solving an expression means you simplify as much as you can Simplify -(3x + 5) - 4x + 3 -7x - 2 J 50/(5 + x) = 10 x = 0

7. Reviewing Laws of Exponents Multiplying exponential expressions with like bases When multiplying exponential expressions with like bases, you should _____________ the exponents. ADD

8. Dividing exponential expressions with like bases When dividing exponential expressions with like bases, you should _______________ the exponents. SUBTRACT

9. Raising a power to a power When raising an exponential expression to a power, you should __________________ the exponents. MULTIPLY

10. Negative exponents Remember: ALWAYS get rid of the negative exponents!!!!! 3 -2 4 -8 -2 -7 -3 3 To get rid of the negative exponent, flip the side of the fraction it is on!

11. Reviewing Laws of Exponents What is the meaning of the expression 2 3 ? What is the value of the expression 2 3 ? How do you know? Recall that in an exponential expression of the form b n, b is called the base and n is called the exponent. You can say that b is raised to the n th power. In expanded form, we would write 5 4 =5∙5∙5∙5. So what about 5 1/2 ? How can we multiply 5 by itself one-half times?

12. Rational Exponents Rational exponents are exponents raised to a rational number, such as 2 1/3 (two to the one- third power) How would you say the following: – 3 2/5 – 8 1/4 – 2 5/8 We will focus on switching the rational exponents into radical form and vice versa

13. Rational Exponents

15. NOTE: There are 3 different ways to write a rational exponent

16. Video on Rational Exponents http://www.youtube.com/watch?v=- T1punCdxas http://www.youtube.com/watch?v=- T1punCdxas

17. Examples:

18. More Examples Rewrite the following exponential expressions as radical expressions. 5 1/3 (xy) 1/2 16x 1/4

19. Examples

20. More Examples Rewrite the following radical expressions as exponential expressions. 3 √x √(6) 3 5 √32

21. ( )

23. Simplify 5 19/3 9 3 x 10/3

24. Review Laws of Exponents

25. Extra Resources http://www.regentsprep.org/Regents/math/algtri g/ATO1/Pracratpower.htm http://www.regentsprep.org/Regents/math/algtri g/ATO1/Pracratpower.htm http://www.mathexpression.com/fractional- exponent.html http://www.mathexpression.com/fractional- exponent.html http://www.onemathematicalcat.org/algebra_bo ok/online_problems/rational_exp.htm http://www.onemathematicalcat.org/algebra_bo ok/online_problems/rational_exp.htm http://math.uww.edu/~mcfarlat/141/expo2.htm http://www.themathpage.com/alg/rational- exponents.htm http://www.themathpage.com/alg/rational- exponents.htm