[tex] {2}^{5} \times {2}^{6} = {2}^{11} [/tex]

[tex] {a}^{4} \times {a}^{6} = {a}^{10} [/tex]

[tex] {d}^{7} \times {d}^{8} = {d}^{15} [/tex]

[tex] {3}^{8} \div {3}^{4} = {3}^{4} \\ {4}^{3} \div 4 = {4}^{2} \\ {a}^{100} \div {a}^{99} = a[/tex]

[tex] {( {b}^{5} )}^{7} = {b}^{35} \\ {( {4}^{5} )}^{2} = {4}^{10} [/tex]

[tex] {2}^{3} + {( - 1)}^{4} = 8 + 1 = 9 \\ 2 \times {3}^{4} - {2}^{5} = 2 \times 81 - 32 = 162 - 32 = 130[/tex]

[tex]3 {a}^{2} ( - \frac{1}{2} a) = - \frac{3}{2} {a}^{3} = - 1.5 {a}^{3} [/tex]

[tex] - 5y( - \frac{1}{15} x {y}^{2} ) = \frac{1}{3} x {y}^{3} [/tex]

[tex] \frac{2}{5} {a}^{3} {b}^{5} \times \frac{3}{2} {a}^{3} b = \frac{3}{5} {a}^{6} {b}^{6} = 0.6 {a}^{6} {b}^{6} [/tex]

[tex] - 14 {a}^{7} {b}^{3} {c}^{11} \times \frac{17}{7} b {c}^{4} = - 34 {a}^{7} {b}^{4} {c}^{15} [/tex]

[tex] {( - 2 {x}^{3}y) }^{3} = - 8 {x}^{9} {y}^{3} [/tex]

[tex] ({ \frac{7}{3} {m}^{24} {n}^{18} ) }^{3} = \frac{343}{27} {m}^{72} {n}^{54} = 12\frac{19}{27} {m}^{72} {n}^{54}[/tex]