[tex] \frac{ {5}^{3}· {5}^{ - 2} }{ {5}^{2} } = [/tex]
[tex] \frac{ {5}^{3 + ( - 2)} }{ {5}^{2} } = [/tex]
[tex] \frac{ {5}^{3 - 2} }{ {5}^{2} } = [/tex]
[tex] \frac{ {5}^{1} }{ {5}^{2} } = [/tex]
[tex] {5}^{1 - 2} = [/tex]
[tex] {5}^{ - 1} [/tex]
[tex]\frac{1}{5}[/tex]
[tex] {3}^{5} · {6}^{ - 5} = [/tex]
[tex] {3}^{5} · \frac{1}{ {6}^{5} } = [/tex]
[tex] \frac{ {3}^{5} }{ {6}^{5} } = [/tex]
[tex] \frac{ {3}^{5} }{ {(2·3)}^{5} } = [/tex]
[tex] \frac{ {3}^{5} }{ {2}^{5} ·{3}^{5} } = [/tex]
[tex] \frac{1}{ {2}^{5} } = [/tex]
[tex] \frac{1}{32} [/tex]
[tex] \frac{( {3}^{2}) ^{3}· {5}^{ - 2} }{ {15}^{ - 1} } = [/tex]
[tex] \frac{ {3}^{2·3}· {5}^{ - 2} }{ {15}^{ - 1} } = [/tex]
[tex] \frac{ {3}^{6} · {5}^{ - 2} }{ {15}^{ - 1} } = [/tex]
[tex] \frac{ {3}^{6}· {5}^{ - 2} }{ {(3·5)}^{ - 1} } = [/tex]
[tex] \frac{ {3}^{6} · {5}^{ - 2} }{ {3}^{ - 1} · {5}^{ - 1} } = [/tex]
[tex] {3}^{6 - ( - 1)} · {5}^{ - 2 - ( - 1)} = [/tex]
[tex] {3}^{6 + 1} · {5}^{ - (2 - 1)} = [/tex]
[tex] {3}^{7} · {5}^{ - 1} = [/tex]
[tex] {3}^{7} · \frac{1}{5} = [/tex]
[tex] \frac{ {3}^{7} }{5} = [/tex]
[tex] \frac{2187}{5} = [/tex]
[tex]437 \frac{2}{5} [/tex]
[tex] \frac{ {2}^{4}· {5}^{ - 3} · {9}^{2} }{8· {3}^{6} · {125}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{4} · {5}^{ - 3} · {3}^{2·2} }{ {2}^{3}· {3}^{6}· {5}^{3( - 1)} } = [/tex]
[tex] \frac{ {2}^{4} · {5}^{ - 3} · {3}^{4} }{ {2}^{3} · {3}^{6} · {5}^{ - 3} } = [/tex]
[tex] \frac{ {2}^{4} · {3}^{4} }{ {2}^{3} · {3}^{6} } = [/tex]
[tex] {2}^{4 - 3} · {3}^{4 - 6} = [/tex]
[tex] {2}^{1} · {3}^{ - 2} [/tex]
[tex]2· \frac{1}{ {3}^{2} } = [/tex]
[tex]2· \frac{1}{9} = [/tex]
[tex] \frac{2}{9} [/tex]
[tex] \frac{ \sqrt[4]{32} · \sqrt{4} }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ \sqrt[4]{32} ·2}{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {32}^{ \frac{1}{4} }·2 }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{5· \frac{1}{4} }·2 }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{5}{4} } ·2}{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{5}{4} + 1} }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{5}{4} + \frac{4}{4} } }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{5 + 4}{4} } }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{9}{4} } }{ {2}^{ - 1} } = [/tex]
[tex] {2}^{ \frac{9}{4} - ( - 1)} = [/tex]
[tex] {2}^{ \frac{9}{4} + 1} = [/tex]
[tex] {2}^{ \frac{9}{4} + \frac{4}{4} } = [/tex]
[tex] {2}^{ \frac{9 + 4}{4} } = [/tex]
[tex] {2}^{ \frac{13}{4} } = [/tex]
[tex] {2}^{3 \frac{1}{4} } = [/tex]
[tex] {2}^{3 + \frac{1}{4} } = [/tex]
[tex] {2}^{3} · {2}^{ \frac{1}{4} } = [/tex]
[tex]8 \sqrt[4]{2} [/tex]
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a
[tex] \frac{ {5}^{3}· {5}^{ - 2} }{ {5}^{2} } = [/tex]
[tex] \frac{ {5}^{3 + ( - 2)} }{ {5}^{2} } = [/tex]
[tex] \frac{ {5}^{3 - 2} }{ {5}^{2} } = [/tex]
[tex] \frac{ {5}^{1} }{ {5}^{2} } = [/tex]
[tex] {5}^{1 - 2} = [/tex]
[tex] {5}^{ - 1} [/tex]
[tex]\frac{1}{5}[/tex]
b
[tex] {3}^{5} · {6}^{ - 5} = [/tex]
[tex] {3}^{5} · \frac{1}{ {6}^{5} } = [/tex]
[tex] \frac{ {3}^{5} }{ {6}^{5} } = [/tex]
[tex] \frac{ {3}^{5} }{ {(2·3)}^{5} } = [/tex]
[tex] \frac{ {3}^{5} }{ {2}^{5} ·{3}^{5} } = [/tex]
[tex] \frac{1}{ {2}^{5} } = [/tex]
[tex] \frac{1}{32} [/tex]
c
[tex] \frac{( {3}^{2}) ^{3}· {5}^{ - 2} }{ {15}^{ - 1} } = [/tex]
[tex] \frac{ {3}^{2·3}· {5}^{ - 2} }{ {15}^{ - 1} } = [/tex]
[tex] \frac{ {3}^{6} · {5}^{ - 2} }{ {15}^{ - 1} } = [/tex]
[tex] \frac{ {3}^{6}· {5}^{ - 2} }{ {(3·5)}^{ - 1} } = [/tex]
[tex] \frac{ {3}^{6} · {5}^{ - 2} }{ {3}^{ - 1} · {5}^{ - 1} } = [/tex]
[tex] {3}^{6 - ( - 1)} · {5}^{ - 2 - ( - 1)} = [/tex]
[tex] {3}^{6 + 1} · {5}^{ - (2 - 1)} = [/tex]
[tex] {3}^{7} · {5}^{ - 1} = [/tex]
[tex] {3}^{7} · \frac{1}{5} = [/tex]
[tex] \frac{ {3}^{7} }{5} = [/tex]
[tex] \frac{2187}{5} = [/tex]
[tex]437 \frac{2}{5} [/tex]
d
[tex] \frac{ {2}^{4}· {5}^{ - 3} · {9}^{2} }{8· {3}^{6} · {125}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{4} · {5}^{ - 3} · {3}^{2·2} }{ {2}^{3}· {3}^{6}· {5}^{3( - 1)} } = [/tex]
[tex] \frac{ {2}^{4} · {5}^{ - 3} · {3}^{4} }{ {2}^{3} · {3}^{6} · {5}^{ - 3} } = [/tex]
[tex] \frac{ {2}^{4} · {3}^{4} }{ {2}^{3} · {3}^{6} } = [/tex]
[tex] {2}^{4 - 3} · {3}^{4 - 6} = [/tex]
[tex] {2}^{1} · {3}^{ - 2} [/tex]
[tex]2· \frac{1}{ {3}^{2} } = [/tex]
[tex]2· \frac{1}{9} = [/tex]
[tex] \frac{2}{9} [/tex]
e
[tex] \frac{ \sqrt[4]{32} · \sqrt{4} }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ \sqrt[4]{32} ·2}{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {32}^{ \frac{1}{4} }·2 }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{5· \frac{1}{4} }·2 }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{5}{4} } ·2}{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{5}{4} + 1} }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{5}{4} + \frac{4}{4} } }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{5 + 4}{4} } }{ {2}^{ - 1} } = [/tex]
[tex] \frac{ {2}^{ \frac{9}{4} } }{ {2}^{ - 1} } = [/tex]
[tex] {2}^{ \frac{9}{4} - ( - 1)} = [/tex]
[tex] {2}^{ \frac{9}{4} + 1} = [/tex]
[tex] {2}^{ \frac{9}{4} + \frac{4}{4} } = [/tex]
[tex] {2}^{ \frac{9 + 4}{4} } = [/tex]
[tex] {2}^{ \frac{13}{4} } = [/tex]
[tex] {2}^{3 \frac{1}{4} } = [/tex]
[tex] {2}^{3 + \frac{1}{4} } = [/tex]
[tex] {2}^{3} · {2}^{ \frac{1}{4} } = [/tex]
[tex]8 \sqrt[4]{2} [/tex]