1. Exponents and Squares Numbers and Operations

2. Exponents and Powers Power – the result of raising a base to an exponent. Ex. 3 2 Base – the number being raised to the exponent. Ex. 3 2 3 is the base Exponent – the number the base is being raised to. Ex. 3 2 2 is the exponent

3. Squares and Cubes Squares and cubes get their name from their figure 3 3 The area of the square is 3 x 3, or 3 2, or 3 squared 3 3 3 The area of the cube is 3 x 3 x 3 or 3 3, or 3 cubed

4. Guided Practice 1. Find 6 squared 2. Find 7 2 3. Find 5 cubed 4. Find 2 3

5. Student Practice Simplify the following expressions. Write your answer in expanded and standard notations. 1)3 3 2)2 3 3)3 2 4)5 2 5)2 10

6. Square Roots Square root – a number which multiplied by itself, gives you the original number. Example: 4 × 4 = 16, so the square root of 16 is 4. Perfect square – a number whose square root is a whole number. Example 9 = 3 x 3

7. Square Roots Square root symbol Number that I want the square root of Square root symbol (Radical Symbol)- the symbol used to denote square root. Example: √ 9 = 3 3 Cube root symbol Number that I want the cube root of Example: 3 √ 8 = 2

8. Guided Practice Evaluate each square root. 1. 2. 3.

9. Student Practice 1. 2. 3. Evaluate each square root. You may use a calculator.

10. Guided Practice 1. 2. 3. 3 √ 27 3 √ 64 3 √343

11. Student Practice 1. 2. 3. Evaluate each cube root. You may use a calculator. 3 √ 512 3 √ 125 3 √ 1331

12. Rules of Exponents 1. When you multiply two terms with the same base, you ADD the exponents. 2. When you have an exponent expression that is raised to a power, you can multiply the exponent and power: 3. When you have anything to the power zero it is just "1" ( x m ) ( x n ) = x ( m + n ) ( x m ) n = x m n x 0 = 1

13. Exponents and Grouping Symbols To evaluate powers involving grouping symbols: (ab) 2 = (ab)(ab) = a x a x b x b = a 2 b 2 The power is applied to each value within the parenthesis. (This applies only when there is one term in parenthesis raised to a power)

14. Guided Practice (7 2 )(7 3 ) (3 2 ) 4 (2 3 b 2 c) 3 (3 2 ) 0

15. Student Practice 1. Simplify (5 3 )(5 4 ) 2. Simplify (4 2 ) 3 3. Simplify (2 3 a 4 b) 2 4. Simplify (5 3 b 2 ) 0

16. Working with Squares Between what two integers does the following fall? : √ 5 √ 4 √ 9 2 3 Answer: √ 5 lies between 2 and 3 Ex: √ 5 1. Identify two closest square roots 2. Evaluate square roots

17. Guided Practice 1. 2. Between what two integers does this fall?

18. Class Practice Between what two integers does this fall? 1. 2.