Multiplying and Dividing Monomials

Multiplying and Dividing Monomials

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

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:
    \(\color{ blue }{x^a×x^b=x^{a+b}}\) , \(\color{ blue }{\frac{x^a}{x^b} =x^{a-b}}\)
    \( \color{ blue }{\frac{1}{x^b} =x^{-b}}, \color{ blue }{(x^a)^b=x^{a×b}}\)
    \( \color{ blue }{(xy)^a= x^a× y^a }\)

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: \((8x^5 )(-2x^4 )=-16x^9 \)

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: \(\frac{-12x^4 y^3}{2xy^2 }=-6x^3 y\)

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: \((-3x^7 )(4x^3 )=-12x^{10}\)

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

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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