How to Multiply and Dividing Monomials

How to Multiply and Dividing Monomials

Monomials are polynomials with only one term. To multiply and divide monomials, use exponent’s rules.

Related Topics

Step by step guide to Multiply and Divide Monomials

  • When you divide two monomials you need to divide their coefficients and then divide their variables.
  • In case of exponents with the same base, you need to subtract their powers.
  • Exponent’s rules:
    \(\color{ blue }{x^a×x^b=x^{a+b}}\) , \(\color{ blue }{\frac{x^a}{x^b} =x^{a-b}}\)
    \( \color{ blue }{\frac{1}{x^b} =x^{-b}}, \color{ blue }{(x^a)^b=x^{a×b}}\)
    \( \color{ blue }{(xy)^a= x^a× y^a }\)

Multiplying and Dividing Monomials – Example 1:

Multiply expressions. \((8x^5 )(-2x^4 )=\)

Solution:

Use multiplication property of exponents: \(\color{blue}{x^a×x^b=x^{a+b}} →x^5×x^4=x^9\)
Then: \((8x^5 )(-2x^4 )=-16x^9 \)

Multiplying and Dividing Monomials – Example 2:

Divide. \(\frac{-12x^4 y^3}{2xy^2 }=\)

Solution:

Use division property of exponents: \(\color{blue}{\frac{x^a}{x^b} =x^{a-b}} , \frac{x^4}{x}= x^{4-1}=x^3 \) and \(\frac{y^3}{y^2} =y\)
Then: \(\frac{-12x^4 y^3}{2xy^2 }=-6x^3 y\)

Multiplying and Dividing Monomials – Example 3:

Multiply expressions. \((-3x^7 )(4x^3 )=\)

Solution:

Use multiplication property of exponents: \(\color{blue}{x^a×x^b=x^{a+b}} →x^7×x^3=x^{10 }\)
Then: \((-3x^7 )(4x^3 )=-12x^{10}\)

Multiplying and Dividing Monomials – Example 4:

Dividing expressions. \(\frac{18x^2 y^5}{2xy^4}=\)

Solution:

Use division property of exponents: \(\color{blue}{\frac{x^a}{x^b} =x^{a-b}} , \frac{x^2}{x}= x^{2-1}=x\) and \(\frac{y^5}{y^4} =y^{5-4}=y\)
Then: \(\frac{18x^2 y^5}{2xy^4}=9xy \)

Exercises for Multiplying and Dividing Monomials

Simplify.

  1. \(\color{blue}{(7x^4y^6)(4x^3y^4)}\)
  2. \(\color{blue}{(15x^4) (3x^9)}\)
  3. \(\color{blue}{(12x^2y^9)(7x^9y^{12})} \\\ \)
  4. \(\color{blue}{\frac{80x^{12 }y^9}{10x^6 y^7}} \\\ \)
  5. \(\color{blue}{\frac{95x^{18 }y^7}{5x^9 y^2}} \\\ \)
  6. \(\color{blue}{\frac{200x^3 y^8}{40x^3 y^7}} \\\ \)

Download Multiplying and Dividing Monomials Worksheet

  1. \(\color{blue}{28x^7y^{10}}\)
  2. \(\color{blue}{45x^{13}}\)
  3. \(\color{blue}{84x^{11}y^{21}}\)
  4. \(\color{blue}{8x^6y^2}\)
  5. \(\color{blue}{19x^9y^5}\)
  6. \(\color{blue}{5y}\)

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