5.1 “ Exponents ” Properties of Exponents: 1.Product of Powers a m · a n = a m+n 2 3 · 2 4 = x...

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5.1 “Exponents” Properties of Exponents: 1. Product of Powers a m · a n = a m+n 2 3 · 2 4 = x 4 · x 8 = 2. Power of a Power (a m ) n = a mn (3 2 ) 3 = (y 5 ) 3 = 3. Power of a Product (ab) m = a m b m (2 · 3) 3 = (5x) 2 = 4. Zero Exponent a 0 = 1 4 0 = (a + b) 0 =

Transcript of 5.1 “ Exponents ” Properties of Exponents: 1.Product of Powers a m · a n = a m+n 2 3 · 2 4 = x...

Page 1: 5.1 “ Exponents ” Properties of Exponents: 1.Product of Powers a m · a n = a m+n 2 3 · 2 4 = x 4 · x 8 = 2.Power of a Power (a m ) n = a mn (3 2 ) 3 =

5.1 “Exponents”Properties of Exponents:1. Product of Powers am · an = am+n 23 · 24 = x4 · x8 =

2. Power of a Power (am)n = amn (32)3 = (y5)3 =

3. Power of a Product (ab)m = ambm

(2 · 3)3 = (5x)2 =

4. Zero Exponent a0 = 1 40 = (a + b)0 =

Page 2: 5.1 “ Exponents ” Properties of Exponents: 1.Product of Powers a m · a n = a m+n 2 3 · 2 4 = x 4 · x 8 = 2.Power of a Power (a m ) n = a mn (3 2 ) 3 =

Exponent Properties Continued5. Negative Exponents a-m =

x-3y5 =

7x-4y0z3 =

6. Quotient of Powers = am-n

=

7. Power of a Quotient =

Page 3: 5.1 “ Exponents ” Properties of Exponents: 1.Product of Powers a m · a n = a m+n 2 3 · 2 4 = x 4 · x 8 = 2.Power of a Power (a m ) n = a mn (3 2 ) 3 =

Examples of Applying Properties1. (-4 · 25)2 =

2.

3. 6 · 10-4

9 · 107

4. b-4b6b7b0

Page 4: 5.1 “ Exponents ” Properties of Exponents: 1.Product of Powers a m · a n = a m+n 2 3 · 2 4 = x 4 · x 8 = 2.Power of a Power (a m ) n = a mn (3 2 ) 3 =

Examples of Applying Properties5. (x-2y-4z)-3

(x5y-3z4)-2

6. c-3d 4c4d-2

7. (-5x-3y6z0)-3

8. (7x-3y7z-4)(3-2x0y-4z-1)-4

Page 5: 5.1 “ Exponents ” Properties of Exponents: 1.Product of Powers a m · a n = a m+n 2 3 · 2 4 = x 4 · x 8 = 2.Power of a Power (a m ) n = a mn (3 2 ) 3 =

Scientific Notation1. A swarm of locusts may contain as many as 85 million locusts per square kilometer and cover an area of 1200 square kilometers. About how many locusts are in such a swarm?

85,000,000 x 1200

Page 6: 5.1 “ Exponents ” Properties of Exponents: 1.Product of Powers a m · a n = a m+n 2 3 · 2 4 = x 4 · x 8 = 2.Power of a Power (a m ) n = a mn (3 2 ) 3 =

Scientific Notation Examples2. (4.5 x 10-4)(8.2 x 1012)

3. 9.8 x 1011

3.6 x 1017

4. The mass of Saturn is about 5.7 x 1026 kilograms. The mass of Jupiter is about 3.7 x 1027 kilograms. About how many times greater is Jupiter’s mass?

Page 7: 5.1 “ Exponents ” Properties of Exponents: 1.Product of Powers a m · a n = a m+n 2 3 · 2 4 = x 4 · x 8 = 2.Power of a Power (a m ) n = a mn (3 2 ) 3 =

Examples of Applying Properties


2.1 Using Properties of Exponents p. 89. Properties of Exponents a&b are real numbers, m&n are integers Product Property : a m * a n =a m+n Power of a.

2.1 Using Properties of Exponents p. 89. Properties of Exponents a&b are real numbers, m&n are integers Product Property : a m * a n =a m+n Power of a.

Welcome to Unit 5 Our Topics for this week Radical Exponents – Review Rules for Exponents – Zero exponents – Negative Exponents Rational Expressions Simplifying.

Welcome to Unit 5 Our Topics for this week Radical Exponents – Review Rules for Exponents – Zero exponents – Negative Exponents Rational Expressions Simplifying.

The Product, Quotient, and Power Rules for Exponents...Quotient rule for exponents Example: p 8 p3 = p8-3 = p5 RULES FOR EXPONENTS If m, n, and k are positive integers, then: 3. Power

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§ 7.2 Rational Exponents. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 7.2 Rational Exponents Rational exponents have been defined in such a way.

§ 7.2 Rational Exponents. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 7.2 Rational Exponents Rational exponents have been defined in such a way.

When multiplying monomials, use the product rule for exponents · When multiplying monomials, use the product rule for exponents. xm • xn = xm+n Multiply coefficients and add exponents

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n th Root & Rational Exponents

n th Root & Rational Exponents

Unit 5‐ Exponents & Polynomials Unit 5 Lesson 1 · Unit 5 Lesson 1 Unit 5‐ Exponents & Polynomials Exponent Rules ... a m a n = a m + n c7 c2 = Product Rule ex) Dec 610:14 AM

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Exponents and Polynomials - Whitesboro Central School … · 2015-07-31 · Exponents and Polynomials 7A Exponents 7-1 Integer Exponents ... EXAMPLE 2 Zero and Negative Exponents

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Grade 9 Math Module 4 - Zero Exponents, Negative Integral Exponents, Rational Exponents, and Radicals

Grade 9 Math Module 4 - Zero Exponents, Negative Integral Exponents, Rational Exponents, and Radicals

Chapter 1 Exponents (Laws of Exponents)

Chapter 1 Exponents (Laws of Exponents)

Day 1 : Laws of Exponents Review Book sections 7.1 and 7.4 a 0 = 1 b -1 = (a m )(a n ) = a m + n = a m – n (ab) m = a m b m.

Day 1 : Laws of Exponents Review Book sections 7.1 and 7.4 a 0 = 1 b -1 = (a m )(a n ) = a m + n = a m – n (ab) m = a m b m.

10.1 Exponents - Big Ideas Math · 410 Chapter 10 Exponents and Scientifi c Notation 10.1 Exponents How can you use exponents to write numbers? Work with a partner. a. Copy and complete

10.1 Exponents - Big Ideas Math · 410 Chapter 10 Exponents and Scientifi c Notation 10.1 Exponents How can you use exponents to write numbers? Work with a partner. a. Copy and complete

Using Properties of Exponents. Properties of Exponents a&b are real numbers, m&n are integers Product Property : a m * a n =a m+n Power of a Power Property.

Using Properties of Exponents. Properties of Exponents a&b are real numbers, m&n are integers Product Property : a m * a n =a m+n Power of a Power Property.

Section R.8 n th Roots; Rational Exponents

Section R.8 n th Roots; Rational Exponents

Laws of Exponentsvcmth00m/Exp3.pdf · Laws of Exponents Addition of Exponents If: a ≠ 0, a m • a n = a m+n Example: ... When taking a Square Root, one question you could ask yourself

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An algorithm for the n Lyapunov exponents of an n ...rgencay/jarticles/pd-nlyapunov.pdfPhysica D 59 (1992) 142-157 North-Holland An algorithm for the n Lyapunov exponents of an n-dimensional

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In this chapter you Exponents and logarithms · 2 Exponents and logarithms 29 A number written in exponent form is one which explicitly looks like: an n is referred to as the exponent

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Exponents and RootsExponents and Rootsmathwithmrbarnes.weebly.com/uploads/1/1/2/1/... · 4A Exponents 4-1 Exponents 4-2 Integer Exponents 4-3 Properties of Exponents 4-4 Multiplying

Exponents and RootsExponents and Rootsmathwithmrbarnes.weebly.com/uploads/1/1/2/1/... · 4A Exponents 4-1 Exponents 4-2 Integer Exponents 4-3 Properties of Exponents 4-4 Multiplying

Holt Algebra 2 1-5 Properties of Exponents In an expression of the form a n, a is the base, n is the exponent, and the quantity a n is called a power.

Holt Algebra 2 1-5 Properties of Exponents In an expression of the form a n, a is the base, n is the exponent, and the quantity a n is called a power.

1/2 Exponents and Radicals 1/3 - dozier math€¦ · 29/09/2017  · C0S7D1.notebook 1 September 29, 2017 Chapter 0 Section 7 Exponents and Radicals √b = b1/n n Square root = 1/2

1/2 Exponents and Radicals 1/3 - dozier math€¦ · 29/09/2017  · C0S7D1.notebook 1 September 29, 2017 Chapter 0 Section 7 Exponents and Radicals √b = b1/n n Square root = 1/2