Exponents and Monomials

Operations with Monomials

​Here we will review and practice

• Identifying monomials

• Adding monomials

• Subtracting monomials

• Multiplying monomials

• Dividing monomials

What is a monomial?

Categorize

Options (14)

5

x

5x

5x²

5x²y

5xyz

$$\frac{x}{5}$$  

5 + x

$$\frac{5}{x}$$  

-10

5x + 2

5x^-3

x + y + z

4x² + 2y

Categorize each as a MONOMIAL or NOT A MONOMIAL

Monomial

Not a Monomial

Multiple Choice

Which statement is true about the expression shown?

• A monomial with a coefficient of x, an exponent of two, and a base of three.

• A monomial with a coefficient of two, an exponent of three, and a base of x.

• A monomial with a coefficient of three, an exponent of x, and a base of two.

• A monomial with an exponent of three, a coefficient of 2, and a base of 2x

Adding and Subtracting Monomials

To add or subtract monomials, combine like terms by adding or subtracting their coefficients.

Remember: like terms must have the same variable(s) raised to the same exponent(s).

Multiple Choice

Which expression is equivalent to:
d + d + d + 3 + 2

• 3d + 5
• $$d^3+5$$

• $$3d^3+5$$

• 3d + 4

Multiple Choice

Simplify the algebraic expression by combining like terms:

$$3x\ +\ 5y\ -\ 3x\ +\ 2y$$  

• $$x\ +\ 7y$$  

• $$-x\ +10y$$  

• $$7y$$  

• $$6x\ +7y$$  

Multiple Choice

Rewrite the expression by combining like terms.
4x² – 2x² + 2y + 6y² – y + x²

• 3x² + 3xy + 6y
• 6y² + 2xy + 2x
• 7x² + 35x
• 3x² + 6y² + y

Multiple Choice

Simplify the following monomial: $$16x^2y-4xy^2-5x^2y+10xy^2$$  

• $$6xy^2+21x^2y$$  

• $$11x^2y\ +6xy^2$$  

• $$6x^2y+11xy^2$$  

Multiple Choice

Find the sum of 16y² and -5y².

• -11y²

• 21y²

• 11y²

• 16y² - 5y²

Multiple Choice

Subtract -2x from -8x

• $$-10x$$

• $$10x$$

• $$6x$$

• $$-6x$$

Multiple Choice

Simplify: 10m²n + 7mn² - m²n

• 9m²n + 7mn²

• 16m²n

• 17m²n - mn²

• No change

Multiple Choice

From $$-9xy^2$$ subtract  $$6xy^2$$  

• $$-3xy^2$$  

• $$3xy^2$$  

• $$-15xy^2$$  

• $$15xy^2$$  

Multiple Select

Apply what you know.

Select all that represent the perimeter of the triangle.

• $$4m^2+3mn^2+7mn^2$$

• $$10mn^2+4m^2$$

• $$14mn^2$$

• $$10mn^4+4m^2$$

Multiple Choice

What is the perimeter for the given rectangle:

• 6x³ - 9x² + 10x - 15
• 6x² + 1x - 15
• 6x² + 4x + 4
• 6x³ + 1x² - 15x

Multiplying Monomials

​To multiply monomials

• multiply coefficients

• keep base the same

• add the exponents

Multiple Choice

(3c²)(10c⁷)

• 13c⁹
• 30c⁵
• 30c⁹
• -30c⁹

Multiple Choice

$$\left(-2x^3y^2\right)\left(5xy^4\right)$$  

• $$3x^3y^8$$  

• $$3x^4y^6$$  

• $$-10x^3y^8$$  

• $$-10x^4y^6$$  

Multiple Choice

Find the missing exponent.

$$h^2\ \times\ h^?\ =\ h^7$$

• $$3$$

• 2

• 5

• 9

Math Response

Simpify $$\left(2xy^2\right)\left(3x^2\right)$$

Type answer here

Correct Answer: 6x^3y^2

Deg^°

Rad

Multiple Choice

$$m^{-5}\times\ m^{-2}$$  Simplify. Hint: Use product rule first, then negative rule!

• $$m^{-3}$$  
  

• $$m^7$$  
  

• $$\frac{1}{m^7}$$  
  

• $$\frac{1}{m^3}$$  
  

Multiple Choice

Rewrite using the same base:
5⁶ ⋅ 5^-2 ⋅ 5^-1

• 5^-3
• 125³

• 5³
• 5^-2

Multiple Choice

Simplify (-7y²)(5y⁴)

• -35y⁶
• -2y⁶
• -35y⁸
• -2y⁸

Math Response

Simplify:

$$6x^2y\ \cdot\ -2y\cdot\ \ \frac{1}{3}x^3$$

Type answer here

Correct Answer: -4x^5y^2

Deg^°

Rad

Multiple Choice

Simplify. Hint: do product rule first, then negative rule!

• $$42x^5$$

  
  

• $$\frac{42}{x^5}$$

• $$\frac{42}{x^{-5}}$$

• $$\frac{1}{42x^5}$$

Dividing Monomials

​To divide monomials

• divide coefficients

• keep base the same

• subtract the exponents

Multiple Choice

Simplify. Express using exponents. $$\frac{2^9}{2^3}$$  

• $$2^{12}$$  

• $$2^6$$  

• $$9^7$$  

• 1⁷

Multiple Choice

Simplify. Express using exponents. $$\frac{12n^5}{4n^2}$$  

• $$8n^3$$  

• $$3n^3$$  

• $$3n^7$$  

Math Response

Simplify. Express using exponents.

Placeholder

Type answer here

Correct Answer: 6x^{10}y^6

Deg^°

Rad

Math Response

Simplify: $$\frac{30x^3y^5}{10x^2y^3}$$  

Type answer here

Correct Answer: 3xy^2

Deg^°

Rad

Multiple Choice

Simplify
$$\frac{10x^8y^5}{4x^2y^5}$$  

• $$6x^6y$$  

• $$\frac{5x^6}{2}$$  

• $$\frac{5x^6y}{2}$$  

• $$6x^6$$  

Multiple Choice

• m⁴
• m⁶
• m¹⁰
• 1/m⁶

Multiple Choice

Simplify the following monomials: $$\frac{21m^8n^5}{27m^5n^4}$$  

• $$\frac{7}{9}m^3n$$  

• $$-6m^3n$$  

• $$\frac{9}{7}m^3n$$  

Multiple Choice

Simplify. Assume no denominator is equal to 0.

$$\frac{24mn^{-9}}{12mn^{-11}}$$  

**Remember:  Divide/reduce coefficients, subtract exponents, and then move negative exponents to the opposite spot.**

• $$\frac{12m^2}{n^{20}}$$  

• $$2n^2$$  

• $$2mn^2$$  

Multiple Choice

Simplify. Assume no denominator is equal to 0.

$$\frac{48x^6y^7z^5}{6xy^7z^6}$$  


**Remember:  Divide/reduce coefficients, subtract exponents, and then move negative exponents to the opposite spot.**

• $$42x^7y^{14}z^{11}$$  

• $$8x^5yz^{-1}$$  

• $$\frac{8x^5}{z}$$