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![\boxed{{a}^{b} \: ^{.} \: {a}^{c} = {a}^{b + c} } \boxed{{a}^{b} \: ^{.} \: {a}^{c} = {a}^{b + c} }](https://tex.z-dn.net/?f=++%5Cboxed%7B%7Ba%7D%5E%7Bb%7D+%5C%3A+++%5E%7B.%7D+%5C%3A+%7Ba%7D%5E%7Bc%7D++%3D++%7Ba%7D%5E%7Bb+%2B+c%7D++%7D)
![\boxed{\frac{ {a}^{b} }{ {a}^{c} } = {a}^{b - c} } \boxed{\frac{ {a}^{b} }{ {a}^{c} } = {a}^{b - c} }](https://tex.z-dn.net/?f=++%5Cboxed%7B%5Cfrac%7B+%7Ba%7D%5E%7Bb%7D+%7D%7B+%7Ba%7D%5E%7Bc%7D+%7D++%3D+++%7Ba%7D%5E%7Bb+-+c%7D+%7D)
![\boxed{{( {a}^{b} )}^{c} = {a}^{b\: ^{.} \:c} } \boxed{{( {a}^{b} )}^{c} = {a}^{b\: ^{.} \:c} }](https://tex.z-dn.net/?f=++%5Cboxed%7B%7B%28+%7Ba%7D%5E%7Bb%7D+%29%7D%5E%7Bc%7D++%3D++%7Ba%7D%5E%7Bb%5C%3A+++%5E%7B.%7D+%5C%3Ac%7D+%7D)
▪Soluciones:
![a). \\ {( - 3)}^{2} {( - 3)}^{3} {( - 3)}^{4} = \\ \\ {( - 3)}^{2 + 3 + 4} = \\ \\ \boxed{ \boxed{ {( - 3)}^{9} }} a). \\ {( - 3)}^{2} {( - 3)}^{3} {( - 3)}^{4} = \\ \\ {( - 3)}^{2 + 3 + 4} = \\ \\ \boxed{ \boxed{ {( - 3)}^{9} }}](https://tex.z-dn.net/?f=a%29.+%5C%5C++%7B%28+-+3%29%7D%5E%7B2%7D++%7B%28+-+3%29%7D%5E%7B3%7D++%7B%28+-+3%29%7D%5E%7B4%7D++%3D++%5C%5C++%5C%5C++%7B%28+-+3%29%7D%5E%7B2+%2B+3+%2B+4%7D++%3D++%5C%5C++%5C%5C++%5Cboxed%7B+%5Cboxed%7B+%7B%28+-+3%29%7D%5E%7B9%7D+%7D%7D)
![b). \\ {( {x}^{3} )}^{2} ( { {x}^{4} )}^{3} = \\ \\ {x}^{6} \: ^{.} \: {x}^{12} = \\ \\ {x}^{12 + 6} = \\ \\ \boxed{ \boxed{ {x}^{18} }} b). \\ {( {x}^{3} )}^{2} ( { {x}^{4} )}^{3} = \\ \\ {x}^{6} \: ^{.} \: {x}^{12} = \\ \\ {x}^{12 + 6} = \\ \\ \boxed{ \boxed{ {x}^{18} }}](https://tex.z-dn.net/?f=b%29.+%5C%5C++%7B%28+%7Bx%7D%5E%7B3%7D+%29%7D%5E%7B2%7D+%28+%7B+%7Bx%7D%5E%7B4%7D+%29%7D%5E%7B3%7D++%3D++%5C%5C++%5C%5C++%7Bx%7D%5E%7B6%7D+++%5C%3A++%5E%7B.%7D++%5C%3A++%7Bx%7D%5E%7B12%7D++%3D++%5C%5C++%5C%5C++%7Bx%7D%5E%7B12+%2B+6%7D++%3D++%5C%5C++%5C%5C++%5Cboxed%7B+%5Cboxed%7B+%7Bx%7D%5E%7B18%7D+%7D%7D)
![c). \\ \frac{ {( - 6)}^{9} }{ {( - 6)}^{3} } = \\ \\ {( - 6)}^{9 - 3} = \\ \\ \boxed{ \boxed{ {( - 6)}^{6} }} c). \\ \frac{ {( - 6)}^{9} }{ {( - 6)}^{3} } = \\ \\ {( - 6)}^{9 - 3} = \\ \\ \boxed{ \boxed{ {( - 6)}^{6} }}](https://tex.z-dn.net/?f=c%29.+%5C%5C+++%5Cfrac%7B+%7B%28+-+6%29%7D%5E%7B9%7D+%7D%7B+%7B%28+-+6%29%7D%5E%7B3%7D+%7D++%3D++%5C%5C++%5C%5C++%7B%28+-+6%29%7D%5E%7B9+-+3%7D++%3D++%5C%5C++%5C%5C+%5Cboxed%7B+%5Cboxed%7B++%7B%28+-+6%29%7D%5E%7B6%7D+%7D%7D)
![d). \\ \frac{ {5}^{6} \: ^{.} \: {5}^{4} \: ^{.} \: {5}^{8} }{ {5}^{2} \: ^{.} \: {5}} = \\ \\ \frac{ {5}^{6} \: ^{.} \: {5}^{3}\: ^{.} \: {5}^{1} \: ^{.} \: {5}^{8} }{ {5}^{3} } = \\ \\ {5}^{6} \: ^{.} \: {5}^{1} \: ^{.} \: {5}^{8} = \\ \\ {5}^{6 + 1 + 8} = \\ \\ \boxed{ \boxed{{5}^{15} }} d). \\ \frac{ {5}^{6} \: ^{.} \: {5}^{4} \: ^{.} \: {5}^{8} }{ {5}^{2} \: ^{.} \: {5}} = \\ \\ \frac{ {5}^{6} \: ^{.} \: {5}^{3}\: ^{.} \: {5}^{1} \: ^{.} \: {5}^{8} }{ {5}^{3} } = \\ \\ {5}^{6} \: ^{.} \: {5}^{1} \: ^{.} \: {5}^{8} = \\ \\ {5}^{6 + 1 + 8} = \\ \\ \boxed{ \boxed{{5}^{15} }}](https://tex.z-dn.net/?f=d%29.+%5C%5C++%5Cfrac%7B+%7B5%7D%5E%7B6%7D++%5C%3A+%5E%7B.%7D+++%5C%3A+%7B5%7D%5E%7B4%7D++%5C%3A+++%5E%7B.%7D+%5C%3A+%7B5%7D%5E%7B8%7D+++%7D%7B+%7B5%7D%5E%7B2%7D++%5C%3A++%5E%7B.%7D++%5C%3A++%7B5%7D%7D++%3D++%5C%5C++%5C%5C++%5Cfrac%7B+%7B5%7D%5E%7B6%7D+%5C%3A+++%5E%7B.%7D+%5C%3A+%7B5%7D%5E%7B3%7D%5C%3A+++%5E%7B.%7D+%5C%3A+%7B5%7D%5E%7B1%7D+%5C%3A+++%5E%7B.%7D+%5C%3A+%7B5%7D%5E%7B8%7D++%7D%7B+%7B5%7D%5E%7B3%7D+%7D++%3D++%5C%5C++%5C%5C++%7B5%7D%5E%7B6%7D+%5C%3A+++%5E%7B.%7D+%5C%3A+%7B5%7D%5E%7B1%7D+%5C%3A+++%5E%7B.%7D+%5C%3A+%7B5%7D%5E%7B8%7D++%3D++%5C%5C++%5C%5C++%7B5%7D%5E%7B6+%2B+1+%2B+8%7D++%3D++%5C%5C++%5C%5C+++%5Cboxed%7B+%5Cboxed%7B%7B5%7D%5E%7B15%7D+%7D%7D)
![e). \\ {2}^{ {3}^{2} } \: ^{.} \: {2}^{ {2}^{3} } = \\ \\ {2}^{6} \: ^{.} \: {2}^{6} = \\ \\ {2}^{6 + 6} = \\ \\ \boxed{\boxed{{2}^{12} }} e). \\ {2}^{ {3}^{2} } \: ^{.} \: {2}^{ {2}^{3} } = \\ \\ {2}^{6} \: ^{.} \: {2}^{6} = \\ \\ {2}^{6 + 6} = \\ \\ \boxed{\boxed{{2}^{12} }}](https://tex.z-dn.net/?f=e%29.+%5C%5C++%7B2%7D%5E%7B+%7B3%7D%5E%7B2%7D+%7D+%5C%3A+++%5E%7B.%7D+%5C%3A+%7B2%7D%5E%7B+%7B2%7D%5E%7B3%7D+%7D++%3D++%5C%5C++%5C%5C++%7B2%7D%5E%7B6%7D+%5C%3A+++%5E%7B.%7D+%5C%3A+%7B2%7D%5E%7B6%7D++%3D++%5C%5C++%5C%5C++%7B2%7D%5E%7B6+%2B+6%7D++%3D++%5C%5C++%5C%5C++++%5Cboxed%7B%5Cboxed%7B%7B2%7D%5E%7B12%7D+%7D%7D)
![f). \\ { [ {({a}^{ 3 })}^{2} \: ^{.} \: {({a}^{2} })^{5}]}^{3} = \\ \\{ ({a}^{6} \: ^{.} \: {a}^{10} ) }^{3} = \\ \\{ ( {a}^{16} ) }^{3} = \\ \\ {a}^{16\: ^{.} \:3} \\ \\ \boxed{ \boxed{ {a}^{48} }} f). \\ { [ {({a}^{ 3 })}^{2} \: ^{.} \: {({a}^{2} })^{5}]}^{3} = \\ \\{ ({a}^{6} \: ^{.} \: {a}^{10} ) }^{3} = \\ \\{ ( {a}^{16} ) }^{3} = \\ \\ {a}^{16\: ^{.} \:3} \\ \\ \boxed{ \boxed{ {a}^{48} }}](https://tex.z-dn.net/?f=f%29.++%5C%5C+++%7B+%5B+%7B%28%7Ba%7D%5E%7B+3+%7D%29%7D%5E%7B2%7D+%5C%3A+++%5E%7B.%7D+%5C%3A+%7B%28%7Ba%7D%5E%7B2%7D+%7D%29%5E%7B5%7D%5D%7D%5E%7B3%7D++%3D++%5C%5C++%5C%5C%7B+%28%7Ba%7D%5E%7B6%7D++%5C%3A+++%5E%7B.%7D+%5C%3A+%7Ba%7D%5E%7B10%7D+%29+%7D%5E%7B3%7D++%3D++%5C%5C++%5C%5C%7B+%28+%7Ba%7D%5E%7B16%7D+%29+%7D%5E%7B3%7D++%3D++%5C%5C++%5C%5C++%7Ba%7D%5E%7B16%5C%3A+++%5E%7B.%7D+%5C%3A3%7D++%5C%5C++%5C%5C++%5Cboxed%7B+%5Cboxed%7B+%7Ba%7D%5E%7B48%7D+%7D%7D)
° Propiedades de Potenciación:
▪Soluciones:
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