Multiplication by a Monomial

Multiplying Monomials

​What is a monomial?

Multiple Select

Identify all monomials.

• a⁷ - 3a + 1

• 15a⁸

• 5 - a⁸

• 7a + 5a¹²

• $$\frac{3}{4}a^2$$  

First, let's review exponents

​x² = x ∙ x​

​​x³ = x ∙ x ∙ x

x⁴ = ? ​

​So what about...

​​x² ∙ x³ = ?

​​

​

​Is there a shortcut?
What do you notice about the exponents and number of x's?

​

​Rule: When multiplying terms with the same base, ​

keep the base and ADD the exponents​

Multiple Choice

Simplify: $$d^4\cdot d^5$$  

• 2d⁴
• d⁹
• d²
• 2d

Multiple Choice

Simplify: $$n^2\ \cdot\ n^4$$  

• 2n²

• n⁸

• n⁶

• 2n⁸

Multiple Choice

Simplify: $$\left(-2\right)^3\ \cdot\ \left(-2\right)^6$$  

• $$\left(-2\right)^9$$  

• $$\left(-2\right)^{18}$$  

• $$\left(-4\right)^{18}$$  

• $$\left(4\right)^9$$  

​​What about this?

​​What about this?

Solution:​

Multiple Choice

$$6x^7\times4x^2$$  

• 10x⁹
• 24x¹⁴
• 24x⁹
• 10x¹⁴

Multiple Choice

$$\left(-7y^3\right)\left(5y^2\right)$$  

• -35y⁶
• -35y⁵
• -2y⁶
• -2y⁵

Multiple Choice

$$\left(-x^5\right)\left(y^3\right)$$  

• -x^8y
• -xy⁸
• -x⁵y³
• -(xy)⁸

Multiple Choice

$$9xy^2\cdot9x^5y^2$$  

• 81x⁶y⁴
• 18x⁶y⁶
• 9x⁶y⁴
• none of the above

Multiple Choice

$$7e^3\cdot10e^3f^5$$  

• 70e³f⁶

• 17e³f⁸

• 70e⁶f⁵

• none of the above

Multiple Choice

$$10xy^3\cdot8x^5y^3$$  

• 80xy³
• 80x⁶y³
• 80x⁶y⁶
• none of the above

Multiple Choice

$$\left(-4a\right)\left(3abc\right)$$  

• -12abc
• -12bc
• -4a²bc
• -12a²bc