[tex] {3}^{6} \times {3}^{ - 2} = {3}^{6 - 2} = {3}^{4} [/tex]
[tex] {( {5}^{3} )}^{ - 2} = {5}^{3 \times (- 2)} = {5}^{ - 6} [/tex]
[tex] \frac{ {4}^{ - 3} }{ {4}^{5} } = {4}^{ - 3 - 5} = {4}^{ - 8} [/tex]
[tex] {( \frac{1}{3} )}^{2} = {3}^{ - 2} [/tex]
[tex] {( - 2)}^{3} \times {5}^{3} = {( (- 2) \times 5)}^{3} = {( - 10)}^{3} [/tex]
[tex] {3}^{ - 6} \times {3}^{8} \times {3}^{ - 3} = {3}^{ - 6 + 8 - 3} = {3}^{ - 1} [/tex]
[tex] {2}^{4} \times {2}^{2} \times {3}^{3} = {2}^{4 + 2} \times {3}^{3} = {2}^{6} \times {3}^{3} \\ = {2}^{2 \times 3} \times {3}^{3} \\ = { ({2}^{2})}^{3} \times {3}^{3} \\ = {4}^{3} \times {3}^{3} \\ = {(4 \times 3)}^{3} \\ = {12}^{3} [/tex]
[tex] {( {3}^{3} \times {15}^{ - 5} \times 5)}^{2} \\ = {( {3}^{2} \times 3 \times {15}^{ - 4} \times \frac{1}{15} \times 5)}^{2} \\ = {( {3}^{2} \times {15}^{ - 4} )}^{2} \\ = {( \frac{ {3}^{2} }{ {( {15}^{2} )}^{2} } )}^{2} \\ = {({ (\frac{3}{225} )}^{2})}^{2} \\ = { \frac{3}{225} }^{4} \\ = {75}^{ - 4} [/tex]
