Question

алгебра помогите пожалуйста........​

Answer 1

1)

$5 {(5 {a}^{ - 3} )}^{ - 2} {a}^{ - 2} = {5}^{1} \times {5}^{ - 2} \times {a}^{( - 3) \times ( - 2)} \times {a}^{ - 2} = {5}^{1 + ( - 2)} \times {a}^{6} \times {a}^{ - 2} = {5}^{ - 1} \times {a}^{6 + ( - 2)} = \frac{1}{5} \times {a}^{4} = \frac{ {a}^{4} }{5}$

при $a = {(0.2)}^{ - 1} = {( \frac{1}{5} )}^{ - 1} = \frac{1}{ \frac{1}{5} } = 5$,

$\frac{ {a}^{4} }{5} = \frac{ {5}^{4} }{5} = {5}^{4 - 1} = {5}^{3} = 125$

2)

${(0.5 {a}^{ - 2} )}^{ - 2} \div {(32 {a}^{5} )}^{3} = ({(0.5)}^{ - 2} \times {a}^{( - 2) \times ( - 2)} ) \div ( {32}^{3} \times {a}^{5 \times 3} ) = ( {( \frac{1}{2} )}^{ - 2} \times {a}^{4} ) \div ( {( {2}^{5} )}^{3} \times {a}^{15} ) = ( \frac{1}{ \frac{1}{ {2}^{ 2} } } \times {a}^{4} ) \div ( {2}^{5 \times 3} \times {a}^{15} ) = ( {2}^{2} \times {a}^{4} ) \div ( {2}^{15} \times {a}^{15} ) = {2}^{2 - 15} \times {a}^{4 - 15} = {2}^{ - 13} \times {a}^{ - 11} = \frac{1}{ {2}^{13} {a}^{11} }$

при $a = {(0.5)}^{ - 4} = {( \frac{1}{2} )}^{ - 4} = \frac{1}{ \frac{1}{ {2}^{4} } } = {2}^{4}$,

$\frac{1}{ {2}^{13} {a}^{11} } = \frac{1}{ {2}^{13} \times {( {2}^{4} )}^{11} } = \frac{1}{ {2}^{13} \times {2}^{4 \times 11} } = \frac{1}{ {2}^{13} \times {2}^{44} } = \frac{1}{ {2}^{13 + 44} } = \frac{1}{ {2}^{57} }$