Question

Necesito ayuda, gracias.

Answer 1

▪A tomar en cuenta:

° Propiedades de Potenciación:

$\boxed{{a}^{b} \: ^{.} \: {a}^{c} = {a}^{b + c} }$

$\boxed{\frac{ {a}^{b} }{ {a}^{c} } = {a}^{b - c} }$

$\boxed{{( {a}^{b} )}^{c} = {a}^{b\: ^{.} \:c} }$


▪Soluciones:
$a). \\ {( - 3)}^{2} {( - 3)}^{3} {( - 3)}^{4} = \\ \\ {( - 3)}^{2 + 3 + 4} = \\ \\ \boxed{ \boxed{ {( - 3)}^{9} }}$


$b). \\ {( {x}^{3} )}^{2} ( { {x}^{4} )}^{3} = \\ \\ {x}^{6} \: ^{.} \: {x}^{12} = \\ \\ {x}^{12 + 6} = \\ \\ \boxed{ \boxed{ {x}^{18} }}$


$c). \\ \frac{ {( - 6)}^{9} }{ {( - 6)}^{3} } = \\ \\ {( - 6)}^{9 - 3} = \\ \\ \boxed{ \boxed{ {( - 6)}^{6} }}$

$d). \\ \frac{ {5}^{6} \: ^{.} \: {5}^{4} \: ^{.} \: {5}^{8} }{ {5}^{2} \: ^{.} \: {5}} = \\ \\ \frac{ {5}^{6} \: ^{.} \: {5}^{3}\: ^{.} \: {5}^{1} \: ^{.} \: {5}^{8} }{ {5}^{3} } = \\ \\ {5}^{6} \: ^{.} \: {5}^{1} \: ^{.} \: {5}^{8} = \\ \\ {5}^{6 + 1 + 8} = \\ \\ \boxed{ \boxed{{5}^{15} }}$


$e). \\ {2}^{ {3}^{2} } \: ^{.} \: {2}^{ {2}^{3} } = \\ \\ {2}^{6} \: ^{.} \: {2}^{6} = \\ \\ {2}^{6 + 6} = \\ \\ \boxed{\boxed{{2}^{12} }}$


$f). \\ { [ {({a}^{ 3 })}^{2} \: ^{.} \: {({a}^{2} })^{5}]}^{3} = \\ \\{ ({a}^{6} \: ^{.} \: {a}^{10} ) }^{3} = \\ \\{ ( {a}^{16} ) }^{3} = \\ \\ {a}^{16\: ^{.} \:3} \\ \\ \boxed{ \boxed{ {a}^{48} }}$