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.

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

### Download Multiplying and Dividing Monomials Worksheet

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