Law of Exponents: Product and Quotient Rule

4.01 Laws of Exponents

Product Rule, Quotient Rule, Power Rules, & Zero and One Exponent

Practice!

Zero and One Exponent

Multiple Choice

Zero Exponent Law states that _____ becomes a 1.

• the exponent
• the base
• nothing
• the whole term

Multiple Choice

One Exponent Law states that raising a term to the power of 1 becomes ______.

• the exponent

• the base

• one

• the whole term

• zero

Multiple Choice

(5³x²y⁴)⁰

• 5xy
• 1
• 0
• 5

Multiple Choice

Which is greater, 2654⁰ or 5¹?

• 2654⁰

• 5¹

• They are the same

Go to notes!

Product and Quotient Rules

Practice

Product and Quotient Rules

Multiple Choice

Product Rule states: keep the base the same and do this to the exponents.

• multiply

• add

• subtract

• divide

Multiple Choice

Quotient Rule states: keep the base the same and do this to the exponents.

• multiply

• add

• subtract

• divide

Multiple Choice

Simplify:
(x³y²)(xy⁴)

• x³y⁸
• x⁴y⁶
• x³y⁶
• x⁴y⁸

Multiple Choice

Simplify:
2a⁷ ÷ 2a³

• a⁴
• 1/a⁴
• 2a⁴
• a^7/3

Multiple Choice

Simplify:
3p² x 2p⁴q²

• 6p^-2q²
• 6p²q²
• 6p⁸q²
• 6p⁶q²

Multiple Choice

Simplify:
x⁵ ÷ x²

• x⁷
• x³
• x¹⁰
• x^2.5

Multiple Choice

Simplify:
(x³)(x²)

• x⁵
• x⁶
• x
• x^1.5

Go back to notes!

Power Rule

Practice!

Power Rule

Multiple Choice

Power Rule states: keep the base the same and do this to the exponents.

• multiply

• add

• subtract

• divide

Multiple Choice

Simplify:
(x³)⁴

• x⁷
• x¹²
• x^-1
• x^3/4

Multiple Choice

Simplify: (4x)³

• 7x³

• 64x³

• 12x³

• 16x³

Multiple Choice

Simplify:
(3t²)³

• 9t⁶
• 9t⁵
• 27t⁶
• 27t⁵

Multiple Choice

Simplify:
3(x³y²)²

• 3x⁶y⁴
• 3x⁵y⁴
• 9x⁶y⁴
• 9x⁵y⁴

Practice!

All Rules

Multiple Choice

Which expression is equivalent to the given?

Multiple Choice

Which expression is equivalent to the given?

Multiple Choice

• a⁸b¹³
• a²b⁷
• a¹⁵b³⁰

Multiple Choice

Using the rules of exponents, simplify the following expression. Your answer should be in exponential form.

• 7³ x 5²

• 7⁴ x 58

• 7³ x 5⁴

• 7² x 5⁴

Multiple Choice

• 4⁹
• 4⁴⁴
• 4²¹
• 4¹⁵

Multiple Choice

Simplify:
(x³y²)(xy⁴)

• x³y⁸
• x⁴y⁶
• x³y⁶
• x⁴y⁸