Question

Prove : the whether it is true or false
​

Answer 1

Answer:

follow the steps :-

${ (\frac{5}{7}) }^{7} \times { (\frac{5}{7} )}^{ - 7} - { (\frac{3}{19} )}^{2} \times {( \frac{3}{19} )}^{ - 2} = 0$

${ (\frac{5}{7}) }^{7 + ( - 7)} - {( \frac{3}{19} )}^{2 + ( - 2)} = 0$

${ (\frac{5}{7} )}^{0} - { (\frac{3}{19} )}^{0} = 0$

$1 - 1 = 0$

$0 = 0 \: \: \: \: \: \: \: \:( hence \: proved) \: .$

Answer 2

$\sf \rightarrow \quad \bigg( \dfrac{5}{7} \bigg)^{7} \times \bigg( \dfrac{7}{5} \bigg) ^{7} - \bigg( \dfrac{3}{19} \bigg) ^{2} \times \bigg( \dfrac{19}{3} \bigg)^{2} = 0 \\ \\ \sf \rightarrow \quad \bigg( \frac{ \cancel{5}}{ \cancel{7}} \times \frac{ \cancel{7}}{ \cancel{5}} \bigg)^{7} - \bigg( \frac{ \cancel{3}}{ \cancel{19}} \times \frac{ \cancel{19}}{ \cancel{3}} \bigg)^{2} = 0 \\ \\ \sf \rightarrow \quad {1}^{7} - {1}^{2} = 0 \\ \\ \sf \rightarrow \quad 0 = 0 \\ \sf \: \: \: \: Hence , \: Proved \\ \\ \underline{ \sf Properties \: Used} \\ \hookrightarrow \quad \sf {a}^{m} \times {b}^{m} = {(a \times b)}^{m}$