Quotient of Powers Worksheet
This worksheet focuses on understanding and applying the quotient of powers rule for exponents at a Grade 9 level.
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Quotient of Powers Rule
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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 \( \frac{m^{12}}{m^4} \)?
\( m^{16} \)
\( m^8 \)
\( m^3 \)
\( m^{-8} \)
5. What is the simplified form of \( \frac{15x^9}{3x^2} \)?
\( 5x^{11} \)
\( 12x^7 \)
\( 5x^7 \)
\( 5x^{4.5} \)
6. When dividing powers with the same base, you the exponents.
7. The quotient of \( \frac{p^8}{p^5} \) is .
8. \( \frac{k^6}{k^6} = k^0 = 1 \)
True
False
9. \( \frac{b^4}{b^9} = b^5 \)
True
False
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)