Multiplying Monomials Worksheets - Free Printable

You've uploaded a worksheet titled “Multiplying Monomials”, and it contains 10 problems. Let’s solve each one step by step, explaining the rules used.

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📌 Key Rules for Multiplying Monomials:

1. Multiply coefficients (the numbers).
2. Add exponents of like bases (using the rule: \( x^a \cdot x^b = x^{a+b} \)).
3. Keep variables that don’t match as they are.
4. Simplify if possible (combine like terms or reduce fractions).

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## ✔ Problem-by-Problem Solutions:

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1. \( \frac{1}{4}x^2 \cdot \frac{1}{5}x^3 \)

- Coefficients: \( \frac{1}{4} \cdot \frac{1}{5} = \frac{1}{20} \)
- Variables: \( x^2 \cdot x^3 = x^{2+3} = x^5 \)
- Answer: \( \boxed{\frac{1}{20}x^5} \)

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2. \( -2y \cdot \frac{1}{2}y \cdot 9y \)

- Coefficients: \( -2 \cdot \frac{1}{2} \cdot 9 = (-1) \cdot 9 = -9 \)
- Variables: \( y \cdot y \cdot y = y^3 \)
- Answer: \( \boxed{-9y^3} \)

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3. \( 7 \cdot -6x^2 \cdot -2x^2 \)

- Coefficients: \( 7 \cdot (-6) \cdot (-2) = 7 \cdot 12 = 84 \)
- Variables: \( x^2 \cdot x^2 = x^4 \)
- Answer: \( \boxed{84x^4} \)

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4. \( -\frac{3}{4} \cdot -32x^2 \)

- Coefficients: \( -\frac{3}{4} \cdot -32 = \frac{3}{4} \cdot 32 = 3 \cdot 8 = 24 \)
- Variable: \( x^2 \) (only one term has variable)
- Answer: \( \boxed{24x^2} \)

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5. \( \frac{4}{5}x^3 \cdot \frac{1}{8}x^5 \)

- Coefficients: \( \frac{4}{5} \cdot \frac{1}{8} = \frac{4}{40} = \frac{1}{10} \)
- Variables: \( x^3 \cdot x^5 = x^8 \)
- Answer: \( \boxed{\frac{1}{10}x^8} \)

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6. \( 3x^2 \cdot -3x^3 \)

- Coefficients: \( 3 \cdot (-3) = -9 \)
- Variables: \( x^2 \cdot x^3 = x^5 \)
- Answer: \( \boxed{-9x^5} \)

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7. \( -14y \cdot \frac{1}{2}y^2 \)

- Coefficients: \( -14 \cdot \frac{1}{2} = -7 \)
- Variables: \( y \cdot y^2 = y^3 \)
- Answer: \( \boxed{-7y^3} \)

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8. \( \frac{3}{4}x^2 \cdot \frac{2}{3}x^3 \cdot \frac{1}{2}x^4 \)

- Coefficients: \( \frac{3}{4} \cdot \frac{2}{3} \cdot \frac{1}{2} \)

→ Simplify step-by-step:

\( \frac{3}{4} \cdot \frac{2}{3} = \frac{6}{12} = \frac{1}{2} \)

Then \( \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} \)

- Variables: \( x^2 \cdot x^3 \cdot x^4 = x^{2+3+4} = x^9 \)
- Answer: \( \boxed{\frac{1}{4}x^9} \)

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9. \( -\frac{1}{2}x^2 \cdot -\frac{2}{3}x^4 \)

- Coefficients: \( -\frac{1}{2} \cdot -\frac{2}{3} = \frac{2}{6} = \frac{1}{3} \)
- Variables: \( x^2 \cdot x^4 = x^6 \)
- Answer: \( \boxed{\frac{1}{3}x^6} \)

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10. \( 6x^2 \cdot -8x^3 \)

- Coefficients: \( 6 \cdot (-8) = -48 \)
- Variables: \( x^2 \cdot x^3 = x^5 \)
- Answer: \( \boxed{-48x^5} \)

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## ✔ Final Answers Summary:

| Problem | Answer |
|---------|------------------|
| 1 | \( \frac{1}{20}x^5 \) |
| 2 | \( -9y^3 \) |
| 3 | \( 84x^4 \) |
| 4 | \( 24x^2 \) |
| 5 | \( \frac{1}{10}x^8 \) |
| 6 | \( -9x^5 \) |
| 7 | \( -7y^3 \) |
| 8 | \( \frac{1}{4}x^9 \) |
| 9 | \( \frac{1}{3}x^6 \) |
| 10 | \( -48x^5 \) |

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Let me know if you’d like to see this as a printable answer key or need help with dividing monomials next! 😊