[tex]i) \sqrt{ \frac{ {3}^{8} }{ {5}^{6} } } = \frac{ \sqrt{ {3}^{8} } }{ \sqrt{ {5}^{6} } } = \frac{ {3}^{ \frac{8}{2} } }{ {5}^{ \frac{6}{2} } } = \frac{ {3}^{4} }{ {5}^{3} } = \frac{81}{125} [/tex]
[tex]j) \sqrt{ \frac{ {4}^{3} }{ {9}^{5} } } = \frac{ \sqrt{ {4}^{3} } }{ \sqrt{ {9}^{5} } } = \frac{ \sqrt{ {( {2}^{2}) }^{3} } }{ \sqrt{ {( {3}^{2} )}^{5} } } = \frac{ \sqrt{ {2}^{2 \times 3} } }{ \sqrt{ {3}^{2 \times 5} } } [/tex]
[tex] = \frac{ \sqrt{ {2}^{6} } }{ \sqrt{ {3}^{10} } } = \frac{ {2}^{ \frac{6}{2} } }{ {3}^{ \frac{10}{2} } } = \frac{ {2}^{3} }{ {3}^{5} } = \frac{8}{243} [/tex]
[tex]k) \sqrt{ \frac{ {3}^{6} \times {2}^{4} }{ {5}^{2} } } = \frac{ \sqrt{ {3}^{6} \times {2}^{4} } }{ \sqrt{ {5}^{2} } } = \frac{ \sqrt{ {3}^{6} } \times \sqrt{ {2}^{4} } }{ \sqrt{ {5}^{2} } } [/tex]
[tex] = \frac{ {3}^{ \frac{6}{2} } \times {2}^{ \frac{4}{2} } }{ {5}^{ \frac{2}{2} } } = \frac{ {3}^{3} \times {2}^{2} }{ {5}^{1} } = \frac{27 \times 4}{5} = \frac{108}{5} [/tex]
[tex]l) \sqrt{ \frac{ {14}^{2} }{ {11}^{2} \times {3}^{2} } } = \frac{ \sqrt{ {14}^{2} } }{ \sqrt{ {11}^{2} \times {3}^{2} } } = \frac{ \sqrt{ {14}^{2} } }{ \sqrt{ {(11 \times 3)}^{2} } } [/tex]
[tex] = \frac{ \sqrt{ {14}^{2} } }{ \sqrt{ {33}^{2} } } = \frac{ {14}^{ \frac{2}{2} } }{ {33}^{ \frac{2}{2} } } = \frac{ {14}^{1} }{ {33}^{1} } = \frac{14}{33} [/tex]
