Lesson 39: Using the Distributive Property to Simplify Rational Expressions — Practice Questions

1. 1. Simplify the expression $\frac{5a^3b^{-2}}{c^{-4}}$ so it contains only positive exponents. The simplified form is ___.

2. 2. Which expression is equivalent to $7k^{-3}$ and contains only positive exponents?

   • A. $\frac{1}{7k^3}$
   • B. $\frac{7}{k^3}$
   • C. $-7k^3$
   • D. $\frac{k^3}{7}$

3. 3. Which expression is the simplified form of $\frac{m^5 p^{-2}}{n^{-4}}$ with only positive exponents?

   • A. $\frac{m^5 n^4}{p^2}$
   • B. $\frac{m^5}{n^4 p^2}$
   • C. $m^5 n^4 p^2$
   • D. $\frac{n^4 p^2}{m^5}$

4. 4. Simplify the expression $x^{-1}y(x^2y^{-1} - 4y^{-3}z)$. Write the result using only positive exponents. The simplified form is ___.

5. 5. Simplify the expression $\frac{p^{-3}}{q}\left(p^5q^2 - \frac{r^{-4}}{p}\right)$ using only positive exponents.

   • A. $p^2q - \frac{1}{p^4qr^4}$
   • B. $p^2q - \frac{p^2}{qr^4}$
   • C. $p^{-2}q - \frac{r^4}{p^4q}$
   • D. $p^2q^3 - \frac{1}{p^2qr^4}$

6. 6. Use the distributive property to simplify the expression. Your answer should be in simplest form. $\frac{p^3}{q} \left( \frac{p^2}{q^4} + \frac{5}{p} \right) = \_\_\_$

7. 7. Which expression is equivalent to $\frac{x^2}{y^4} \left( \frac{y^5}{x} + \frac{2x^3}{y} \right)$ after simplifying?

   • A. $xy + \frac{2x^5}{y^5}$
   • B. $x^3y + \frac{2x^5}{y^4}$
   • C. $xy + \frac{2x^3}{y^4}$
   • D. $\frac{x}{y} + \frac{2x^6}{y^4}$

8. 8. Simplify the following expression using the distributive property: $\frac{k}{j^2} \left( \frac{j^3}{h} - 4k^2 \right) = \_\_\_$

9. 9. What is the result of simplifying the expression $\frac{mn}{p^2} \left( \frac{p^3}{mn} + \frac{2m}{p} \right)$?

   • A. $p + \frac{2m^2n}{p^3}$
   • B. $1 + \frac{2m^2n}{p^3}$
   • C. $p + \frac{2m}{p^2}$
   • D. $mnp + \frac{2m^2n}{p^3}$

10. 10. Apply the distributive property to simplify the expression below. $\frac{r^4}{s^2} \left( \frac{3s}{t} + \frac{s^3}{r^2} \right) = \_\_\_$