1.
[tex] \frac{ {3}^{20} }{ {3}^{22} - {3}^{21} } = \\ \frac{ {3}^{20} }{(3 - 1) \times {3}^{22} } = \\ \frac{1}{2 \times 3} = \\ \frac{1}{6} [/tex]
2.
[tex] \frac{ {6}^{13} }{ {3}^{14} } \times \frac{ {5}^{10} }{ {10}^{12} } = \\ \frac{ {2}^{13} \times {3}^{13} }{ {3}^{14} } \times \frac{ {5}^{10} }{ {2}^{12} \times {5}^{12} } = \\ \frac{2}{3} \times \frac{1}{ {5}^{2} } = \\ \frac{2}{3} \times \frac{1}{25} = \\ \frac{2}{75} [/tex]
3.
[tex] \frac{ {2}^{19} \times {15}^{3} \times {3}^{15} }{ {6}^{18} \times {5}^{2} } = \\ \frac{ {2}^{19} \times {3}^{3} \times {5}^{3} \times {3}^{15} }{ {3}^{18} \times {2}^{18} \times {5}^{2} } = \\ \frac{2 \times {3}^{3} \times 5 }{ {3}^{3} } = \\ 2 \times 5 = \\10 [/tex]
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Verified answer
1.
[tex] \frac{ {3}^{20} }{ {3}^{22} - {3}^{21} } = \\ \frac{ {3}^{20} }{(3 - 1) \times {3}^{22} } = \\ \frac{1}{2 \times 3} = \\ \frac{1}{6} [/tex]
2.
[tex] \frac{ {6}^{13} }{ {3}^{14} } \times \frac{ {5}^{10} }{ {10}^{12} } = \\ \frac{ {2}^{13} \times {3}^{13} }{ {3}^{14} } \times \frac{ {5}^{10} }{ {2}^{12} \times {5}^{12} } = \\ \frac{2}{3} \times \frac{1}{ {5}^{2} } = \\ \frac{2}{3} \times \frac{1}{25} = \\ \frac{2}{75} [/tex]
3.
[tex] \frac{ {2}^{19} \times {15}^{3} \times {3}^{15} }{ {6}^{18} \times {5}^{2} } = \\ \frac{ {2}^{19} \times {3}^{3} \times {5}^{3} \times {3}^{15} }{ {3}^{18} \times {2}^{18} \times {5}^{2} } = \\ \frac{2 \times {3}^{3} \times 5 }{ {3}^{3} } = \\ 2 \times 5 = \\10 [/tex]