Advanced Algebra NotesSection 5.1: Finding Rational Zeros

When we multiply two powers together that have the same base we use the_____________________________ to make calculating our answer easy. Laws of ExponentsLet a and b be real numbers and let m and n be integers.

Property of Powers: am an = am+n Ex:

Power of a Power: (am)n = amn Ex:

Power of a Product: (ab)m = ambm Ex:

Negative Exponent: a-m = , Ex:

Zero Exponent: a0 = 1 , Ex:

Quotient of Powers: = am-n Ex:

Power of a Quotient: Ex:

Laws of Exponents

4 7 11x x x

23 6x x

62 12 6x y x y

9

4

q

q q5

4

3

x

y

4

43

x

y

04 1

2

1

323 1

9

Examples: Simplify the numerical expressions.

1. (-32 5)3 2. - 2

__________________ is a way to write very large or very small numbers so you can use the laws of exponents to make your calculations easier. Scientific Notation: c 10n , where 1 < c < 10 and n is and integer Examples: Simplify and write your answer in scientific notation. 3. (5.4 104)(2.5 10-7) 4.

Scientific notation

(−36 ⋅ 53 )(−729 ⋅ 125 )

-91,125

1− 8

3− 4

34

18 81

13.5 ⋅ 10−3

1.35 ⋅ 101 ⋅ 10−3

1.35 ⋅ 10−24 ⋅

1

104

4 ⋅ 10−4

You can use the properties of exponents to simplify algebraic expressions. A simplified expression contains only __________ exponents. Examples: Simplify the algebraic expressions. 5. x-6 x5 x3 6. (7y2z5)(y-4z-1) 7. 8.

positive

𝑥2 7 𝑦−2𝑧 4

7 𝑧4

𝑦2

𝑠9

𝑡−12

𝑠9 𝑡12

4− 2𝑥−8 𝑦 4

6− 2𝑥−6 𝑦− 12

62 𝑥6 𝑦4 𝑦12

42𝑥8

36 𝑦16

16 𝑥29 𝑦16

4 𝑥2

( 15𝑎2𝑏−2−3 𝑎𝑏− 3 )− 2

( 3 𝑧𝑎−4 )2( 3 𝑥− 12𝑦 𝑧−32 𝑥 𝑦7 )

− 3

Please add these two problems

PowerMultiply Divide

Add Subtract

Nothing

Helping Hand for Exponents

Find the operation then take a step down and do that to the exponents.

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