Question

Hola! necesito que me ayuden a resolver estas expresiones de potencias
Es para hoy!

Answer 1

Respuesta:

${( {( - 2)}^{2} \times {2}^{3} \times {3}^{10} )}^{2} = {((4) \times {2}^{3} \times {3}^{10}) }^{2} = {( {2}^{2} \times {2}^{3} \times {3}^{10}) }^{2} \\ {({2}^{5} \times {3}^{10} )}^{2} = {2}^{10} \times {3}^{20} = {(2 \times {3}^{2} )}^{10} = {(2 \times 9)}^{10} \\ = {18}^{10}$

$\frac{ {( {5}^{8} \times {7}^{6} \times 5 \times {7}^{10})}^{3} }{( {7}^{12} \times {5}^{5} \times {5}^{3} \times {7}^{4})^{3} } = \frac{ {( {5}^{9} \times {7}^{16})}^{3} }{ {( {5}^{8} \times {7}^{16})}^{3} } = \frac{ {5}^{27} \times {7}^{48} }{ {5}^{24} \times {7}^{48} } \\ {5}^{27 - 24} \times {7}^{48 - 48} = {5}^{3} \times {7}^{0} = 125 \times 1 = 125$

$\frac{( {(a \times {b}^{2}) }^{3} \times {( {a}^{2} \times b) }^{2}) ^{5} }{ {( {a}^{2} \times b \times {( - a)}^{4})}^{2} \times {( {( - a)}^{3} \times ( - b)^{2})}^{2} } = \frac{ {( {a}^{3} \times {b}^{6} \times {a}^{4} \times {b}^{2}) }^{5} }{ {a}^{4} \times {b}^{2} \times {a}^{8} \times {a}^{6} \times {b}^{4} } \\ \frac{ {a}^{7 \times 5} \times {b}^{8 \times 5} }{ {a}^{18} \times {b}^{6} } = \frac{ {a}^{35} \times {b}^{40} }{{a}^{18} \times {b}^{6}} = {a}^{35 - 18} \times {b}^{40 - 6} \\ = {a}^{17} \times {b}^{34}$