Lesson 1: Properties of Exponents — Practice Questions

1. 1. Simplify the expression $(6x^3 - 3x^3)x^3$.

   • A. $3x^3$
   • B. $3x^5$
   • C. $6x^3 - 3x^5$
   • D. $3x^6$

2. 2. Simplify the expression $\left(\frac{-3c^3}{d^4}\right)^2$.

   • A. $\frac{9c^6}{d^8}$
   • B. $\frac{-9c^6}{d^8}$
   • C. $\frac{9c^5}{d^6}$
   • D. $\frac{-6c^6}{d^8}$

3. 3. Simplify the expression $6x^3 - 3x^6$ as much as possible. The simplified expression is ___.

4. 4. Find the value of $n$ that satisfies the equation $\frac{c^8}{c^n} = c^2$. $n = $ ___.

5. 5. Find the value of $n$ that makes the equation $\frac{c^8}{c^n} = c^2$ true. $n = $ ___.

6. 6. Simplify the expression $-4p(-p^2q^2)^2(-q^3)^2$. The simplified expression is ___.

7. 7. Simplify the expression $4x^2(2x^4)$. The simplified form is $8x^{\_\_\_}$.

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

9. 9. Simplify the expression $[ab^2(a^2b)^3]^3$. The simplified expression is ___.

10. 10. Simplify the expression $2a(a^2)^4 + 3a^2(a^6) - a^2(a^2)^3$. The simplified expression is ___.