QuestionAugust 26, 2025

17. CREATE Write two algebraic expressions whose quotients are y^7

17. CREATE Write two algebraic expressions whose quotients are y^7
17. CREATE Write two algebraic expressions whose quotients are y^7

Solution
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Answer

Two algebraic expressions are y^{10} and y^{3}. Explanation 1. Define the Quotient The quotient of two expressions is given by \frac{\text{numerator}}{\text{denominator}} = y^7. 2. Choose a Numerator Select a numerator, e.g., y^{10}. 3. Determine the Denominator To achieve the quotient y^7, set the denominator as y^{3} because y^{10} \div y^{3} = y^{10-3} = y^7. 4. Verify the Expression Check that \frac{y^{10}}{y^{3}} = y^{7} holds true.

Explanation

1. Define the Quotient<br /> The quotient of two expressions is given by $\frac{\text{numerator}}{\text{denominator}} = y^7$.<br /><br />2. Choose a Numerator<br /> Select a numerator, e.g., $y^{10}$.<br /><br />3. Determine the Denominator<br /> To achieve the quotient $y^7$, set the denominator as $y^{3}$ because $y^{10} \div y^{3} = y^{10-3} = y^7$.<br /><br />4. Verify the Expression<br /> Check that $\frac{y^{10}}{y^{3}} = y^{7}$ holds true.
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