Multiplying exponents

Multiplying exponents

By Susan Kahler

Multiple Choice

Simplify the following:

y⁴ ⋅ y¹²

• y¹⁶

• y³

• 16y

• y⁴⁸

Multiple Choice

Simplify the following:

x ∙ x ∙ x ∙ x ∙ x ∙ x

• x⁶

• 6x

• x³

• 6x⁶

Multiple Choice

Simplify the expression: r⁶ ⋅ r² ⋅ r³

• r⁶⁺²⁺³

• r¹¹

• 11r

Multiple Choice

x^{20 .} x¹⁰

• x³⁰

• x²⁰⁰

• 2x³⁰

• x¹⁰

​(3x³)(7x²)

You can see how the rule above works if you expand this out and use the commutative property of multiplication which states that the order in which you multiply two numbers does not affect the outcome. ​

3⋅​7⋅x⋅x⋅x⋅x⋅x = 21x⁵

​2 more examples:

Multiple Choice

(2n⁴ )( 5n⁴)

• 7n⁴
• 10n¹⁶
• 10n⁸
• none of the above

Multiple Choice

(6k² )( k)

• 6
• 6k
• 6k²
• 6k³

Multiple Choice

(5b²  )(8b)

• 45b³
• 40b³
• 13b²
• 5b³

Multiple Choice

6x * 6x³

• 12x³
• 36x⁴
• 42x⁴
• x²

Multiple Choice

$$6r\cdot5r^2$$  

• 30r³

• 30r²

• 11r³

• 11r²

​You can do this with multiple variables as well. Let's look at this in expanded form.

(-6ab²) = -6⋅​a⋅b⋅b

(4a³b⁶) = 4⋅​a⋅a⋅a⋅b⋅b⋅b⋅b⋅b⋅b

(-6ab²)(4a³b⁶) =-6⋅4⋅a⋅a⋅a⋅a⋅b⋅b⋅b⋅b⋅b⋅b⋅b⋅b = -24a⁴b⁸

Multiple Choice

What is equivalent to

$$3x^2y\cdot6xy^3$$  

• $$9x^3y^4$$  

• $$9x^3y^3$$  

• $$18x^3y^4$$  

• $$18x^3y^3$$  

Multiple Choice

What is equivalent to

$$5m^4n^3\cdot8m^5n^4z$$  

• $$40m^9n^7$$  

• $$13m^8n^7z$$  

• $$13m^9n^7z$$  

• $$40m^9n^7z$$  

Multiple Choice

9x⁵y²⋅ 9xy²

• 81x⁶y⁴
• 81x⁵y⁶
• 9x⁶y⁴
• none of the above

Multiple Choice

 10u³v⁵ ⋅ 7v³

• 70u³v¹⁵
• 17u³v⁸
• 70u³v⁸
• none of the above

Multiple Choice

8x⁵y³⋅ 10xy³

• 80xy³
• 80x⁵y⁹
• 80x⁶y⁶
• none of the above

Multiple Choice

(2a²b⁴z)(6a³b²z⁵)

• 8a⁵b⁶z⁶
• 12a⁶b⁸z⁵
• 12a⁵b⁶z⁶
• 8a⁶b⁸z⁵

Multiple Choice

$$6m^3n^3\cdot8m^2n^3$$  

• 48m⁵n⁹

• 48m⁶n⁶

• 48m⁵n⁶

• none of the above