Quotient of Powers Worksheet

Quotient of Powers Rule

Simplify each expression using the quotient of powers rule. Show your work where indicated.

1. Simplify: \( \frac{x^7}{x^3} \)

2. Simplify: \( \frac{y^{10}}{y^2} \)

3. Simplify: \( \frac{a^5 b^8}{a^2 b^3} \)

4. Which expression is equivalent to \( \frac{m^{12}}{m^4} \)?

5. What is the simplified form of \( \frac{15x^9}{3x^2} \)?

6. When dividing powers with the same base, you   the exponents.

7. The quotient of \( \frac{p^8}{p^5} \) is  .

8. \( \frac{k^6}{k^6} = k^0 = 1 \)

9. \( \frac{b^4}{b^9} = b^5 \)

10. A rectangular garden has an area of \( 24x^5 \) square meters. If the width of the garden is \( 3x^2 \) meters, what is the length of the garden? (Hint: Area = Length × Width)