Algebra 1 worksheet focused on multiplying exponents, featuring ten practice problems with solutions for students.

Here are the step-by-step solutions for each problem on the worksheet.

Rule to remember: When multiplying numbers with the same base, you keep the base and add the exponents.
Formula: $a^m \times a^n = a^{m+n}$

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1. $8^{-14} \times 8^{-10}$
* The bases are both 8.
* Add the exponents: $-14 + (-10) = -24$.
* Result: $8^{-24}$

2. $6^3 \times 6^{-1} \times 6^{-3}$
* The bases are all 6.
* Add the exponents: $3 + (-1) + (-3)$.
* Calculation: $3 - 1 = 2$, and $2 - 3 = -1$.
* Result: $6^{-1}$

3. $5^{-1} \times 5^{-3} \times 5^{-4}$
* The bases are all 5.
* Add the exponents: $-1 + (-3) + (-4)$.
* Calculation: $-1 - 3 = -4$, and $-4 - 4 = -8$.
* Result: $5^{-8}$

4. $(-3)^3 \times (-3)^{-2}$
* The bases are both $(-3)$.
* Add the exponents: $3 + (-2)$.
* Calculation: $3 - 2 = 1$.
* Result: $(-3)^1$ or just $-3$.

5. $4^2 \times 4^3 \times 4^{-5}$
* The bases are all 4.
* Add the exponents: $2 + 3 + (-5)$.
* Calculation: $2 + 3 = 5$, and $5 - 5 = 0$.
* Result: $4^0$. (Note: Any non-zero number to the power of 0 equals 1).
* Simplified Result: $1$

6. $5^3 \times 5^6$
* The bases are both 5.
* Add the exponents: $3 + 6 = 9$.
* Result: $5^9$

7. $8^3 \times 8^2 \times 8^{-4}$
* The bases are all 8.
* Add the exponents: $3 + 2 + (-4)$.
* Calculation: $3 + 2 = 5$, and $5 - 4 = 1$.
* Result: $8^1$ or just $8$.

8. $9^2 \times 9^{-2} \times 9^4$
* The bases are all 9.
* Add the exponents: $2 + (-2) + 4$.
* Calculation: $2 - 2 = 0$, and $0 + 4 = 4$.
* Result: $9^4$

9. $7^3 \times 7^{-2}$
* The bases are both 7.
* Add the exponents: $3 + (-2)$.
* Calculation: $3 - 2 = 1$.
* Result: $7^1$ or just $7$.

10. $2^3 \times 2^{-4} \times 2^3 \times 2^6$
* The bases are all 2.
* Add the exponents: $3 + (-4) + 3 + 6$.
* Calculation: $3 - 4 = -1$. Then $-1 + 3 = 2$. Then $2 + 6 = 8$.
* Result: $2^8$

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Final Answer:
1. $8^{-24}$
2. $6^{-1}$
3. $5^{-8}$
4. $-3$ (or $(-3)^1$)
5. $1$ (or $4^0$)
6. $5^9$
7. $8$ (or $8^1$)
8. $9^4$
9. $7$ (or $7^1$)
10. $2^8$