Exponents and Squares Numbers and Operations

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 is the base Exponent – the number the base is being raised to. Ex is the exponent

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 The area of the cube is 3 x 3 x 3 or 3 3, or 3 cubed

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

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

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

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

Guided Practice Evaluate each square root

Student Practice Evaluate each square root. You may use a calculator.

Guided Practice √ 27 3 √ 64 3 √343

Student Practice Evaluate each cube root. You may use a calculator. 3 √ √ √ 1331

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

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)

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

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

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

Guided Practice Between what two integers does this fall?

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