# Laws of Exponents

Lesson 1

Rules of 1

Any number raised to 1 is equal to the number itself x¹=x

Examples: Common Error: 1.) 4¹= 4 1.) 4¹=4 2.) 5¹= 5 2.) 5¹=5 3.) 146¹=146 3.) 146¹=146

Practice Your Skill!

1.) 391¹=

2.) 45¹=

3.) 678¹=

4.) 99¹=

5.) 34¹=

Lesson 2

Product Rule

To multiply two powers having the same base, add their exponents.

xᵐ * xᵃ = xᵐᶧᵃ

Examples: Common Error:

1.)a² * a¹ = a³ 1.) a² * a¹= 2a⁶ 2.) 5x²yz³ * 4xy³z² = 5*4x²ᶧ¹ + y¹ᶧ³ + z²ᶧ²= 20x³y⁴z⁵ 2.) 5x²yz³ * 4xy³z² = 9x²y³z⁶

Practice Your Skill!

Simplify the following expressions:

1.) 3y²*4y*3y³=

2.) 78x²y * -9y² =

3.) 45b⁸*11b⁷ =

Lesson 3

Power Rule

To raise a power, multiply the exponents

(xᵐ)ᵒ=xᵐᵒ

Examples: Common Error: 1.) (ab)³= a³b³ 1.) (ab)³= a¹ᶧ³b¹ᶧ³= a⁴b⁴ 2.) (3m²n)² = 3²m²˙²n²˙¹= 9m⁴n² 2.) (3m²n)² =3²ᶧ¹m¹ᶧ²n¹ᶧ²= 27m³n³

Practice Your Skill!

1.) (-3pr²)² =

2.) (2a³b²)²=

3.) (6z⁵t²)³ =

4.) (16c⁴g³)⁶=

Lesson 4

Quotient Rule

If x ≠ 0 ; m and n are positive integers.

Case 1: xᵐxᵘ = xᵐ⁻ᵘ where m > n Examples: Common Error: 1.) a⁵a³ = a⁵⁻³ = a² 1.) a⁵a³ = a⁵ᶧ³ = a⁸ 2.) a⁸b⁴a⁵b² = a⁸⁻⁵b⁴⁻² = a³b²...

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