QuestionAugust 26, 2025

Question Simplify, assuming that xgt 0 and ygt 0 (sqrt (300x^28y^28))/(sqrt (3x^14)y^12) Provide your answer below:

Question Simplify, assuming that xgt 0 and ygt 0 (sqrt (300x^28y^28))/(sqrt (3x^14)y^12) Provide your answer below:
Question Simplify, assuming that xgt 0 and ygt 0 (sqrt (300x^28y^28))/(sqrt (3x^14)y^12) Provide your answer below:

Solution
4.5(173 votes)

Answer

10x^7y^8 Explanation 1. Simplify the numerator \sqrt{300x^{28}y^{28}} = \sqrt{300} \cdot \sqrt{x^{28}} \cdot \sqrt{y^{28}} = \sqrt{300} \cdot x^{14} \cdot y^{14} 2. Simplify the denominator \sqrt{3x^{14}y^{12}} = \sqrt{3} \cdot \sqrt{x^{14}} \cdot \sqrt{y^{12}} = \sqrt{3} \cdot x^7 \cdot y^6 3. Divide the simplified expressions \frac{\sqrt{300} \cdot x^{14} \cdot y^{14}}{\sqrt{3} \cdot x^7 \cdot y^6} = \frac{\sqrt{300}}{\sqrt{3}} \cdot \frac{x^{14}}{x^7} \cdot \frac{y^{14}}{y^6} 4. Simplify each component \frac{\sqrt{300}}{\sqrt{3}} = \sqrt{\frac{300}{3}} = \sqrt{100} = 10 \frac{x^{14}}{x^7} = x^{14-7} = x^7 \frac{y^{14}}{y^6} = y^{14-6} = y^8

Explanation

1. Simplify the numerator<br /> $\sqrt{300x^{28}y^{28}} = \sqrt{300} \cdot \sqrt{x^{28}} \cdot \sqrt{y^{28}} = \sqrt{300} \cdot x^{14} \cdot y^{14}$<br /><br />2. Simplify the denominator<br /> $\sqrt{3x^{14}y^{12}} = \sqrt{3} \cdot \sqrt{x^{14}} \cdot \sqrt{y^{12}} = \sqrt{3} \cdot x^7 \cdot y^6$<br /><br />3. Divide the simplified expressions<br /> $\frac{\sqrt{300} \cdot x^{14} \cdot y^{14}}{\sqrt{3} \cdot x^7 \cdot y^6} = \frac{\sqrt{300}}{\sqrt{3}} \cdot \frac{x^{14}}{x^7} \cdot \frac{y^{14}}{y^6}$<br /><br />4. Simplify each component<br /> $\frac{\sqrt{300}}{\sqrt{3}} = \sqrt{\frac{300}{3}} = \sqrt{100} = 10$<br /> $\frac{x^{14}}{x^7} = x^{14-7} = x^7$<br /> $\frac{y^{14}}{y^6} = y^{14-6} = y^8$
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