Lesson 40: Simplifying and Evaluating Expressions Using the Power Property of Exponents — Practice Questions

1. 1. Use the Power of a Power Property to simplify the expression $(p^7)^4$. The simplified expression is ___.

2. 2. Which expression is equivalent to $(y^6)^2$?

   • A. $y^8$
   • B. $y^{12}$
   • C. $2y^6$
   • D. $y^{36}$

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

4. 4. What is the simplified form of $(-5w^2)^3$?

   • A. $-15w^6$
   • B. $125w^6$
   • C. $-125w^6$
   • D. $-125w^5$

5. 5. Simplify the expression $((x^4)^2)^5$.

   • A. $x^{11}$
   • B. $x^{13}$
   • C. $x^{30}$
   • D. $x^{40}$

6. 6. Simplify the expression $\left(\frac{2x^4}{5}\right)^2$. The simplified form is ___.

7. 7. Which of the following expressions is equivalent to $\left(\frac{4p^3}{q^2}\right)^2$?

   • A. $\frac{16p^6}{q^4}$
   • B. $\frac{4p^6}{q^4}$
   • C. $\frac{16p^5}{q^4}$
   • D. $\frac{8p^6}{q^4}$

8. 8. Simplify the expression $\left(\frac{-3m^2}{n^4}\right)^3$. The simplified form is ___.

9. 9. Which of the following correctly shows the first step in simplifying $\left(\frac{a^5}{2b}\right)^4$ using the Power of a Quotient Property?

   • A. $\frac{(a^5)^4}{(2b)^4}$
   • B. $\frac{(a^5)^4}{2b}$
   • C. $\frac{a^5}{(2b)^4}$
   • D. $\frac{a^9}{(2b)^4}$

10. 10. Simplify the expression $\left(\frac{5xy^3}{z^2}\right)^2$.

    • A. $\frac{25x^2y^6}{z^4}$
    • B. $\frac{5x^2y^6}{z^4}$
    • C. $\frac{25y^6}{z^4}$
    • D. $\frac{10x^2y^5}{z^4}$