4.1 Exponents, p168. Find the product │ –7 –7 –7│ = (8) = 4. ÷ (8) = (-6) ⁴ = (–6) (–6) (–6) ● (-6) = -6 ⁴ = –1 ( ● 6 ) = LO: I will evaluate exponents using repeated multiplication & Order of Operations.

Write in exponential form, then simplify. 4(___) + 16 Simplify the _____________ inside the parenthesis. Subtract inside the ________________. Multiply from left to right. 4( 4 – 2 ) + 2 4(___ – ___) + ___ ___ + ___ 2. x(y x – z y ) + x for x = 4, y = 2, and z = 3. y = ____ Substitute, then use Order of Operations, GEMDAS. 1. Reasoning: 3. Discuss whether 3⁹ is the same as 9³ 4. Justify the inequality 4⁶ > 4⁵

The expression (–4) 4 is NOT the same as the expression –4 4. (–4) 4 = (-4) ●(-4) ●(-4) ●(-4) = –4 4 = –1 ● 4 4 = -1(4● 4● 4● 4) = Caution! NO Parentheses ALWAYS = a Negative Answer! Think opposite quantity. WHY? Because you use GEMDAS to evaluate the exponent, THEN multiply by –1. 5. (–5)³ = = 6. –9³ = = 7. – (¾)² = =

Real Life Applications 9. A microscope can magnify a specimen 10³ times. How many time is that? 10. Use the pattern to determine what comes next in this sequence. 8. A cube has a side length of 3 units. What is its volume?

4.6/4.7 Squares and Square Roots, p192/96 Warm Up Simplify = = = = = LO: I will evaluate squares & square roots using exponents with 2 degrees of power. 6. Find the area 1.5 So √ 64 = 8 represents the principal square root; and - √ 64 = -8 represents the negative square root. THEREFORE: You can write √ 64 = ±8, which is read as “The square root of sixty-four is plus or minus eight.”

1.69 = ___ 2 So √1.69 = _____; therefore the window is _____ feet wide. ALWAYS use the PRINCIPAL (positive integer) square root for DISTANCE. √ 16 = The table is __ feet wide, which is less than __ feet. ___ the table _____ fit through the van door. 1. A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening? 4. The floor of a square room has an area of 256 ft². What is the perimeter of the room? 3. Ms. Estefan wants to put a fence around 3 sides of a square vegetable garden that has an area of 225 ft 2. How much fencing does she need? 2. A square window has an area of 1.69 square feet. How wide is the window? 5. A chessboard contains 32 black and 32 white squares. How many squares are along each side of the game board?

RM 4.1 & SR p171 #51-62 even 13. Patterns

(Class work) Use a piece of paper to evaluate the problems on this slide.

perfect between perfect  Square Roots that are ______________ two nonzero integers are estimates.  √between is an IRRATIONAL NUMBERS.  A PERFECT SQUARE is a number that has square roots that are nonzero integers.  √ perfect is a ______________ NUMBER.

Launch LO: I will explore rational numbers using fractions, decimals, & integers.

Explore Whole number ²= perfect square √perfect root = whole number Look for and describe the pattern of the highlighted numbers.

perfect between perfect  Square Roots that are ______________ two nonzero integers are estimates.  √between is an IRRATIONAL NUMBERS.  A PERFECT SQUARE is a number that has square roots that are nonzero integers.  √ perfect is a ______________ NUMBER.

Skills & Modifications A number that is multiplied by itself to form a product is a square root of that product. The radical symbol is used to represent square roots. For nonnegative numbers, the operations of squaring and finding a square root are inverse operations. In other words, for x ≥ 0, Positive real numbers have two square roots. The symbol is used to represent both square roots. A perfect square is a number whose positive (principal) square root is a whole number.

The principal square root of a number is the positive square root and is represented by. A negative square root is represented by –. 4  4 = __ = __ = 4= 4 Positive square root of (–4)( – 4) = (–4) 2 = 16 = (–1)4 – The small number to the left of the root is the index. In a square root, the index is understood to be 2. In other words, is the same as. Writing Math