4.1 Exponents, p168. Find the product.

1. 5 • 5 • 5 • 5

3. │ –7 • –7 • –7│ =

1 8

1 8

2. (8) =

4. ÷ (8) =

(-6)⁴ = (–6) • (–6) • (–6) ● (-6) =

-6⁴ = –1 ( 6 • 6 • 6 ● 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(yx – zy) + x for x = 4, y = 2, and z = 3.y

= ____

Substitute, then use Order of Operations, GEMDAS.

1.

Reasoning:

3. Discuss whether 3 is the same ⁹as 9³

4. Justify the inequality 4 > 4⁶ ⁵

The expression (–4)4 is NOT the same as the expression –44.

(–4)4 = (-4) ●(-4) ●(-4) ●(-4) = –44 = –1 ● 44 = -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.

1. 52 = 2. 82 =

3. 122 = 4. 152 =

5. 202 =

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 ft2. 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 numbersusing fractions, decimals, & integers.

Exploring Rational Numbers-Fractions, Decimals and IntegersSimplify each expression.1. (–9)(–9) 2. 3. 4. Complete the sequence:

Explore

Whole number = perfect square²

√perfect root = whole numberLook 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 Positive squareroot 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