[tex] {3}^{ - 5} \times {9}^{2} = \\ {3}^{ - 5} \times ( {3}^{2} ) {}^{2} = \\ {3}^{ - 5} \times {3}^{4} = \\ {3}^{ - 1} = \\ \frac{1}{3} [/tex]
[tex] {81}^{ - 2} \div {27}^{ - 3} = \\ ( {3}^{4} ) {}^{ - 2} \div ( {3}^{3} ) {}^{ - 3} = \\ {3}^{ - 8} \div {3}^{ - 9} = \\ 3[/tex]
[tex] \frac{ {6}^{4} \times {9}^{ - 3} }{ {4}^{2} } = \\ \frac{ {6}^{4} }{ {4}^{2} \times {9}^{ 3} } = \\ \frac{ {6}^{4} }{16 \times {9}^{3} } = \\ \frac{1296}{16 \times {9}^{3} } = \frac{81}{ {9}^{3} } = \frac{ {9}^{2} }{ {9}^{ 3} } = \frac{1}{9} [/tex]
