4.1 Properties of Exponents PG. 107. Must Have the Same Base to Apply Most Properties.

4.1 Properties of Exponents

PG. 107

Must Have the Same Base to Apply Most Properties

xb

“Product of Powers”

“Power of a Power”

“Power of a Product”

Properties of Exponents

m n m na a a

nm mna a

m m mab a b

“Negative Exponent”

“Zero Exponent”

Properties of Exponents

1 , 0mma aa

0 1, 0a a

“Quotient of Powers”

“Power of a Quotient”

, 0m

m nn

a a aa

, 0m m

m

a a bb b

Properties of Exponents

Investigating Math Activity (p. 101)

GUIDED PRACTICE for Examples 1 and 2

Evaluate the expression. Tell which properties of exponents you used.

1. (42 )3

4096 ; Power of a power property2. (–8)(–8)3

4096 ; Product of a powers property

3. 2 3

9

8729; Power of a quotient property

ANSWER

ANSWER

ANSWER

WARM-UP Standardized Test Practice

SOLUTION

GUIDED PRACTICE for Examples 3, 4, and 5

Simplify the expression. Tell which properties ofexponents you used.

5. x–6x5 x3

x2 ; Product of powers property

6. (7y2z5)(y–4z–1)

7z4

y2; Product of powers property, Negative exponent propertyANSWER

ANSWER

GUIDED PRACTICE for Examples 3, 4, and 5

7. s 3 2

t–4

s6t8 ; Power of a power property, Negative exponent property

8. x4y–2 3

x3y6

; Quotient of powers property, Power of a Quotient property, Negative exponent property

x3 y24 ANSWER

ANSWER

SCIENTIFIC NOTATION Is in the form c x 10n

C is a number between 1 and 9.99……….

n is an integer Positive = bigger number (move right) Negative = smaller number (move left)

SCIENTIFIC NOTATION Examples…

Ex 1) 1,200

Ex 2) 0.0004

Ex 3) 31,200,000

Multiplying Scientific Notation Examples…

Ex 4) (3.2 x 103) (1.4 x 102)

Ex 5) (2.7 x 104) 2

Ex 6) (2.2 x 10-5) (7.4 x 103)

GUIDED PRACTICE for Examples 1 and 2

6 10 – 4

9 107

4.

; quotient of power property 2

3 1011ANSWER

Homework Pg. 110, 1 – 32 all