Verified answer

[tex] {z}^{20} \times {z}^{22} = {z}^{42} [/tex]

[tex] {(z + 2)}^{3} \times {(z + 2)}^{5} = {(z + 2)}^{8} [/tex]

[tex] {y}^{22} = {y}^{4} \times {y}^{5} \times {y}^{x} \\ {y}^{22} = {y}^{9} \times {y}^{x} \\ {y}^{x} = {y}^{22} - {y}^{9} \\ {y}^{x = 13} \\ x = 13[/tex]

[tex] {z}^{5} \div z = {z}^{4} [/tex]

[tex] {k}^{14} \div {k}^{7} \times {k}^{2} = {k}^{7} \times {k}^{2} = {k}^{9} [/tex]

[tex] {(4m {}^{3}) }^{3} = 64 {m}^{9} [/tex]

[tex] \frac{ { {(6}^{5} )}^{ - 6} }{ {6}^{ - 29} } = \frac{ {6}^{ - 30} }{ {6}^{ - 29} } = {6}^{ - 1} = \frac{1}{6} \\ [/tex]

[tex] \frac{ {9}^{ - 6} \times {9}^{14} }{ {81}^{3} } = \frac{ {9}^{8} }{ { ({9}^{2}) }^{3} } = \frac{ {9}^{8} }{ {9}^{6} } = {9}^{2} = 81 \\ [/tex]

[tex] \frac{ ({3}^{ - 3}) {}^{3} \times {7}^{7} }{ {27}^{2} } = \frac{ {3}^{ - 9} \times {7}^{7} }{ ({ {3}^{3}) }^{2} } = \frac{ {3}^{ - 9} \times {7}^{7} }{ {3}^{6} } = {3}^{ - 15} \times {7}^{7} [/tex]

[tex] { {(c}^{2} )}^{4} \times { {(c}^{3} )}^{5} \div { {(c}^{3}) }^{7} = {c}^{8} \times {c}^{15} \div {c}^{21} = {c}^{23} \div {c}^{21} = {c}^{2} [/tex]