Lesson 2: Product of Powers Property — Practice Questions

1. 1. Simplify the expression by using the fourth law of exponents: $(5x)^5$.

   • A. $3125x^5$
   • B. $25x^5$
   • C. $5x^5$
   • D. $3125x$

2. 2. Simplify the expression $(-2ab)^4$.

   • A. $16a^4b^4$
   • B. $-16a^4b^4$
   • C. $8a^4b^4$
   • D. $-8ab^4$

3. 3. Factor the trinomial $4a^2 - 12ab + 9b^2$. The factored form is ___.

4. 4. Simplify the expression $(2ab)^4$ using the power of a product rule. The result is ___.

5. 5. Which expression is equivalent to $(-5x)^3$?

   • A. $-125x^3$
   • B. $125x^3$
   • C. -15x
   • D. $-5x^3$

6. 6. Simplify the expression $(3x^4y)^2$. The simplified form is ___.

7. 7. Which statement correctly describes the difference between $2p^4$ and $(2p)^4$?

   • A. They are equivalent expressions.
   • B. In $2p^4$, only $p$ is raised to the 4th power; in $(2p)^4$, both $2$ and $p$ are.
   • C. In $(2p)^4$, only $p$ is raised to the 4th power.
   • D. $2p^4$ simplifies to $16p^4$.

8. 8. Use the laws of exponents to simplify $(-2m^3n)^4$. The result is ___.

9. 9. Find the value of $n$ that makes the expression $3 \cdot 3^n = 3^4$ true. $n = \_\_\_$

10. 10. Apply the first law of exponents to simplify the product: $5^4 \cdot 5^5 = \_\_\_$