Multiplying Monomials and Powers of Monomials Lesson Plan for 9th ... - Free Printable

Looking at the image you uploaded, it’s a worksheet titled “Multiplying Monomials and Powers of Monomials” from the Jefferson Davis Learning Center. The task is to simplify each expression (problems 1–15) using exponent rules, and match them to the correct answers on the right.

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✔ Let’s solve each problem step by step:

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#### Problem 1: \( 6x^2 \cdot x^3 \)
Use the rule: \( x^a \cdot x^b = x^{a+b} \)
→ \( 6x^{2+3} = 6x^5 \)
✔ Answer: A. \( 6x^5 \)

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#### Problem 2: \( (-3ab^2)(-a^3) \)
Multiply coefficients: \( (-3) \cdot (-1) = 3 \)
Multiply variables: \( a \cdot a^3 = a^4 \), \( b^2 \) stays
→ \( 3a^4b^2 \)
✔ Answer: B. \( 3a^4b^2 \)

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#### Problem 3: \( (2x^3y^2)^3 \)
Apply power to each part:
\( 2^3 = 8 \), \( (x^3)^3 = x^9 \), \( (y^2)^3 = y^6 \)
→ \( 8x^9y^6 \)
✔ Answer: C. \( 8x^9y^6 \)

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#### Problem 4: \( -7(3a^2b)(2ab) \)
First multiply inside: \( 3a^2b \cdot 2ab = 6a^3b^2 \)
Then multiply by -7: \( -7 \cdot 6a^3b^2 = -42a^3b^2 \)
✔ Answer: D. \( -42a^3b^2 \)

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#### Problem 5: \( m^2(-n^3)(-m^2n)(-3) \)
Group coefficients: \( 1 \cdot (-1) \cdot (-1) \cdot (-3) = -3 \)
Variables: \( m^2 \cdot m^2 = m^4 \), \( n^3 \cdot n = n^4 \)
→ \( -3m^4n^4 \)
✔ Answer: E. \( -3m^4n^4 \)

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#### Problem 6: \( k^2 \cdot k^5 \)
→ \( k^{2+5} = k^7 \)
✔ Answer: F. \( k^7 \)

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#### Problem 7: \( (-w^2)^3 \)
Apply power: \( (-1)^3 \cdot (w^2)^3 = -1 \cdot w^6 = -w^6 \)
✔ Answer: G. \( -w^6 \)

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#### Problem 8: \( (p^2q^3)^2 \)
→ \( p^4q^6 \)
✔ Answer: H. \( p^4q^6 \)

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#### Problem 9: \( (-r^2s^3)^4 \)
Even power → negative becomes positive
→ \( r^8s^{12} \)
✔ Answer: I. \( r^8s^{12} \)

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#### Problem 10: \( (2c^3d^2)^3 \)
→ \( 8c^9d^6 \)
✔ Answer: J. \( 8c^9d^6 \)

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#### Problem 11: \( (4a^3bc^2)^2 \)
→ \( 16a^6b^2c^4 \)
✔ Answer: K. \( 16a^6b^2c^4 \)

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#### Problem 12: \( 3ab^2 \cdot 5a^3b \)
Coefficients: \( 3 \cdot 5 = 15 \)
Variables: \( a \cdot a^3 = a^4 \), \( b^2 \cdot b = b^3 \)
→ \( 15a^4b^3 \)
✔ Answer: L. \( 15a^4b^3 \)

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#### Problem 13: \( (w^2z^3)^4 \)
→ \( w^8z^{12} \)
✔ Answer: M. \( w^8z^{12} \)

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#### Problem 14: \( (-2f^2g^3)(-3fg^2)(-f^3g) \)
Coefficients: \( (-2) \cdot (-3) \cdot (-1) = -6 \)
Variables: \( f^2 \cdot f \cdot f^3 = f^6 \), \( g^3 \cdot g^2 \cdot g = g^6 \)
→ \( -6f^6g^6 \)
✔ Answer: N. \( -6f^6g^6 \)

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#### Problem 15: \( (x^2y^3z^2)^2(xy^2z^3) \)
First: \( (x^2y^3z^2)^2 = x^4y^6z^4 \)
Then multiply by \( xy^2z^3 \):
→ \( x^{4+1}y^{6+2}z^{4+3} = x^5y^8z^7 \)
✔ Answer: O. \( x^5y^8z^7 \)

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📋 Final Answer Key:

| Problem | Answer |
|---------|--------|
| 1 | A |
| 2 | B |
| 3 | C |
| 4 | D |
| 5 | E |
| 6 | F |
| 7 | G |
| 8 | H |
| 9 | I |
| 10 | J |
| 11 | K |
| 12 | L |
| 13 | M |
| 14 | N |
| 15 | O |

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✔ All problems are solved using basic exponent rules:
- When multiplying same bases → add exponents.
- When raising a power to a power → multiply exponents.
- Coefficients multiply normally.
- Negative signs follow sign rules (odd power keeps negative, even removes it).

Let me know if you’d like a printable version or further explanation on any step!