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