Question

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Answer 1

QUESTIONS:

$1) \: \: ({ ({ \frac{ - 5}{7}) }^{ - 2}) }^{2} \\ \\ 2) \: \: \: { (\frac{7}{10}) }^{ - 4} \times { (\frac{10}{21} )}^{ - 4}$

ANSWER:

1) 2401 / 625

2) 81

TO FIND:

$1) \: \: ({ ({ \frac{ - 5}{7}) }^{ - 2}) }^{2} \\ \\ 2) \: \: \: { (\frac{7}{10}) }^{ - 4} \times { (\frac{10}{21} )}^{ - 4}$

FORMUALE:

${( \frac{1}{x} )}^{ - m} = {x}^{m}$

EXPLANATION:

$1) \: \: ({ ({ \frac{ - 5}{7}) }^{ - 2}) }^{2} \\ \\ { (\frac{ - 5}{7}) }^{ - 4} \\ \\ { (\frac{ - 7}{5}) }^{4} \\ \\ \frac{ - 7 \times - 7 \times - 7 \times - 7}{5 \times 5 \times 5 \times 5} \\ \\ \frac{49 \times 49}{25 \times 25} \\ \\ \frac{2401}{625}$

$2) \: \: \: { (\frac{7}{10}) }^{ - 4} \times { (\frac{10}{21} )}^{ - 4} \\ \\ {( \frac{10}{7} )}^{4} \times {( \frac{21}{10} )}^{4} \\ \\ \frac{10 \times 10 \times 10 \times 10 \times {(21)}^{4} }{10 \times 10 \times 10 \times 10 \times {(7)}^{4} } \\ \\ \frac{21 \times 21 \times 21 \times 21}{7 \times 7 \times 7 \times 7} \\ \\ 3 \times 3 \times 3 \times 3 \\ \\ 9 \times 9 \\ \\ 81$

$1) \: \: ({ ({ \frac{ - 5}{7}) }^{ - 2}) }^{2} = \frac{2401}{625} \\ \\ 2) \: \: \: { (\frac{7}{10}) }^{ - 4} \times { (\frac{10}{21} )}^{ - 4} =81$

Answer 2

1.${(( { \frac{ - 5}{7}) }^{ - 2}) }^{2}$

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

$= \frac{2401}{625}$

2.${ (\frac{7}{10} )}^{ - 4} \times { (\frac{10}{21}) }^{ - 4}$

$= {( \frac{7}{10} \times \frac{10}{21}) }^{ - 4}$

${ (\frac{1}{3} )}^{ - 4} = {3}^{4}$

$= 81$