Multiplication Exponents Algebra 1 Worksheet Printable - Free Printable

Let's solve each problem on the Algebra 1 Worksheet: Multiplication of Exponents step by step. We'll use the laws of exponents, especially:

> When multiplying powers with the same base, add the exponents:
> $$
> a^m \times a^n = a^{m+n}
> $$

Also recall:
- Negative exponents: $ a^{-n} = \frac{1}{a^n} $
- Any non-zero number to the power of 0 is 1.

---

1. $ 8^{-14} \times 8^{10} $

Same base (8), so add exponents:
$$
8^{-14 + 10} = 8^{-4}
$$

✔ Answer: $ 8^{-4} $ or $ \frac{1}{8^4} $

---

2. $ 6^3 \times 6^1 \times 6^{-3} $

Add exponents:
$$
6^{3+1+(-3)} = 6^{1}
$$

✔ Answer: $ 6^1 = 6 $

---

3. $ 5^1 \times 5^{-3} \times 5^4 $

Add exponents:
$$
5^{1 + (-3) + 4} = 5^{2}
$$

✔ Answer: $ 5^2 = 25 $

---

4. $ (-3)^3 \times (-3)^{-2} $

Same base ($-3$), add exponents:
$$
(-3)^{3 + (-2)} = (-3)^1 = -3
$$

✔ Answer: $ -3 $

---

5. $ 4^{-2} \times 4^3 \times 4^{-5} $

Add exponents:
$$
4^{-2 + 3 + (-5)} = 4^{-4}
$$

✔ Answer: $ 4^{-4} $ or $ \frac{1}{4^4} = \frac{1}{256} $

---

6. $ 5^3 \times 5^6 $

Add exponents:
$$
5^{3+6} = 5^9
$$

✔ Answer: $ 5^9 $

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7. $ 8^3 \times 8^2 \times 8^{-4} $

Add exponents:
$$
8^{3+2+(-4)} = 8^1 = 8
$$

✔ Answer: $ 8 $

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8. $ 9^2 \times 9^{-2} \times 9^4 $

Add exponents:
$$
9^{2 + (-2) + 4} = 9^4
$$

✔ Answer: $ 9^4 $

---

9. $ 7^3 \times 7^{-2} $

Add exponents:
$$
7^{3 + (-2)} = 7^1 = 7
$$

✔ Answer: $ 7 $

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10. $ 2^3 \times 2^{-4} \times 2^3 \times 2^6 $

Add all exponents:
$$
2^{3 + (-4) + 3 + 6} = 2^{8}
$$

✔ Answer: $ 2^8 = 256 $

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✔ Final Answers:

1. $ 8^{-4} $
2. $ 6 $
3. $ 25 $
4. $ -3 $
5. $ \frac{1}{256} $ or $ 4^{-4} $
6. $ 5^9 $
7. $ 8 $
8. $ 9^4 $
9. $ 7 $
10. $ 256 $ or $ 2^8 $

Let me know if you'd like these written in simplified form (like actual numbers) or as fractions!