[tex]( {c}^{7} {)}^{2} \times \frac{c}{( {c}^{5} {)}^{3} } = {c}^{14} \times \frac{c}{ {c}^{15} } = {c}^{14} \times {c}^{ - 14} = {c}^{0} = 1[/tex]
[tex]( {6}^{2} {)}^{6} \times \frac{6}{ {6}^{12} } = {6}^{12} \times {6}^{ - 11} = {6}^{1} = 6[/tex]
[tex] \frac{( {b}^{6} {)}^{4} }{( {b}^{3} {)}^{5} \times b} = \frac{ {b}^{24} }{ {b}^{15} \times b} = \frac{ {b}^{24} }{ {b}^{16} } = {b}^{8} [/tex]
[tex]( {5}^{5} {)}^{2} \times \frac{5}{ {5}^{10} } = {5}^{10} \times {5}^{ - 9} = {5}^{1} = 5[/tex]
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[tex] \frac{ {2}^{12} }{125} \times \frac{ {5}^{5} }{1024} = \frac{ {2}^{12} \times {5}^{5} }{ {5}^{3} \times {2}^{10} } = {2}^{2} \times {5}^{2} = 4 \times 25 = 100[/tex]
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[tex] {125}^{6} = {5}^{18} \\ \frac{1}{5} \times \frac{ {125}^{6} }{1} = \frac{1}{5} \times \frac{( {5}^{3} {)}^{6} }{1} = \frac{1}{5} \times \frac{ {5}^{18} }{1} = {5}^{17} [/tex]
~~~~[tex](64 \times 32 {)}^{6} = ( {2}^{6} \times {2}^{5} {)}^{6} = ( {2}^{11} {)}^{6} = {2}^{66} [/tex]
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6^6^6, 6^66, (6^6)^6, 66^6
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[tex] \frac{625}{ {8}^{3} } \times \frac{ {2}^{12} }{ {5}^{7} } = \frac{ {5}^{4} }{( {2}^{3} {)}^{3} } \times \frac{ {2}^{12} }{ {5}^{7} } = \frac{ {5}^{4} }{ {2}^{9} } \times \frac{ {2}^{12} }{ {5}^{7} } = {5}^{ - 3} \times {2}^{3} [/tex]
