Exponents multiplication worksheet for simplifying algebraic expressions.

Let's solve each problem on the worksheet step by step. The goal is to simplify expressions involving exponents using the laws of exponents.

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🔷 Laws of Exponents Used:

1. $ a^m \times a^n = a^{m+n} $
2. $ (ab)^n = a^n b^n $
3. $ a \times a = a^2 $, etc.
4. Coefficients (numbers) are multiplied separately.

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Now let’s go through each problem:

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1.) $ 5x \times 6x $

- Multiply coefficients: $ 5 \times 6 = 30 $
- Multiply variables: $ x \times x = x^2 $
- ✔ Answer: $ 30x^2 $

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2.) $ 6x^2 \times 3x $

- Coefficients: $ 6 \times 3 = 18 $
- Variables: $ x^2 \times x = x^{2+1} = x^3 $
- ✔ Answer: $ 18x^3 $

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3.) $ 6x^3 \times 2x^2 $

- Coefficients: $ 6 \times 2 = 12 $
- Variables: $ x^3 \times x^2 = x^{3+2} = x^5 $
- ✔ Answer: $ 12x^5 $

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4.) $ 6x \times 3x^2 $

- Coefficients: $ 6 \times 3 = 18 $
- Variables: $ x \times x^2 = x^{1+2} = x^3 $
- ✔ Answer: $ 18x^3 $

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5.) $ 6x^3 \times 6x^2 \times 3x^2 $

- First, multiply coefficients: $ 6 \times 6 \times 3 = 108 $
- Now variables: $ x^3 \times x^2 \times x^2 = x^{3+2+2} = x^7 $
- ✔ Answer: $ 108x^7 $

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6.) $ n^2 \times 3n^2 \times n^2 $

- Coefficients: $ 1 \times 3 \times 1 = 3 $
- Variables: $ n^2 \times n^2 \times n^2 = n^{2+2+2} = n^6 $
- ✔ Answer: $ 3n^6 $

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7.) $ 6n^2 \times 3n^2 \times 6n^2 $

- Coefficients: $ 6 \times 3 \times 6 = 108 $
- Variables: $ n^2 \times n^2 \times n^2 = n^{2+2+2} = n^6 $
- ✔ Answer: $ 108n^6 $

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8.) $ 3n^2 \times 3n \times n $

- Coefficients: $ 3 \times 3 \times 1 = 9 $
- Variables: $ n^2 \times n \times n = n^{2+1+1} = n^4 $
- ✔ Answer: $ 9n^4 $

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9.) $ 4n^3 \times 2n^2 $

- Coefficients: $ 4 \times 2 = 8 $
- Variables: $ n^3 \times n^2 = n^{3+2} = n^5 $
- ✔ Answer: $ 8n^5 $

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10.) $ 4x \times 6x^2 $

- Coefficients: $ 4 \times 6 = 24 $
- Variables: $ x \times x^2 = x^{1+2} = x^3 $
- ✔ Answer: $ 24x^3 $

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✔ Final Answers:

| Problem | Answer |
|--------|----------------|
| 1 | $ 30x^2 $ |
| 2 | $ 18x^3 $ |
| 3 | $ 12x^5 $ |
| 4 | $ 18x^3 $ |
| 5 | $ 108x^7 $ |
| 6 | $ 3n^6 $ |
| 7 | $ 108n^6 $ |
| 8 | $ 9n^4 $ |
| 9 | $ 8n^5 $ |
| 10 | $ 24x^3 $ |

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Let me know if you'd like this formatted as a printable answer sheet!