Question

5 Aplica las propiedado de las potencias y Calcula:
a)
$\frac{ {5}^{7} \times {4}^{7} }{( - 20) ^{7} }$
b)
$\frac{ {4}^{2} \times ( - 3) ^{2} }{ {18}^{2} }$
c)
$\frac{( - 6) ^{5} \times ( - 3) ^{5} }{36 ^{5} }$
d)
$( { \frac{2}{3} })^{6} \div ( { \frac{2}{3} })^{3} \times {6}^{3}$
es urgente
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Answer 1

a)

$= \frac{ {5}^{7} \times {4}^{7} }{( - 20) {}^{7} } \\ = \frac{ {5}^{7} \times {4}^{7} }{ - ( {5}^{7} \times {4}^{7} } \\ = \frac{1}{ - 1} \\ = - 1$

b)

$= \frac{ {4}^{2} \times {( - 3)}^{2} }{ {18}^{2} } \\ = \frac{16 \times 9}{ {9}^{2} \times 4} \\ = {4}^{2 - 1} \times {9}^{1 - 2} \\4 \times {9}^{ - 1} \\ = \frac{4}{9}$

c)

$= \frac{ {( - 6)}^{5} \times {( - 3)}^{5} }{ {36}^{5} } \\ = \frac{ - {6}^{5} \times - {3}^{5} }{ {6}^{10} } \\ = {6}^{5 - 10} \times {3}^{5} \\ = {6}^{ - 5} \times {3}^{5} \\ = {(3 \times 2)}^{ - 5} \times {3}^{5} \\ = {2}^{ - 5} \\ = \frac{1}{32}$