Question

find the value of 1 / 7 power -2 +(1/4) power-3 +(1/13)power -1​

Answer 1

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

$\displaystyle \red{\texttt{Find the value of}} \: \tt{ \purple{ \bigg( \orange{ { \frac{ \blue{1}}{ \blue{7}} \purple{\bigg)}}} }^{ \orange{ - }\blue{2}} } \orange{ \tt + { \purple{\bigg(}\frac{ \blue{1}}{\blue{4}} \purple{\bigg)} }^{ - \blue{3}} } \orange{ \tt + { \purple{\bigg(}\frac{ \blue{1}}{\blue{13}} \purple{\bigg)} }^{ - \blue{1}}. }$

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

$\displaystyle\tt{ \purple{ \bigg( \orange{ { \frac{ \blue{1}}{ \blue{7}} \purple{\bigg)}}} }^{ \orange{ - }\blue{2}} } \orange{ \tt + { \purple{\bigg(}\frac{ \blue{1}}{\blue{4}} \purple{\bigg)} }^{ - \blue{3}} } \orange{ \tt + { \purple{\bigg(}\frac{ \blue{1}}{\blue{13}} \purple{\bigg)} }^{ - \blue{1}} } \: \\ \\ \orange{\tt{ \purple{\implies( { \blue{7}})}^{ \blue{2}} + \: \purple{ ( { \blue{4}})}^{ \blue{3}} + \blue{13} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \orange{\tt{ \purple{\implies} \blue{49} + \blue{64} + \blue{13}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \blue{\tt{ \purple{\implies}126 }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{\boxed{\boxed{\displaystyle\tt{ \purple{ \bigg( \orange{ { \frac{ \blue{1}}{ \blue{7}} \purple{\bigg)}}} }^{ \orange{ - }\blue{2}} } \orange{ \tt + { \purple{\bigg(}\frac{ \blue{1}}{\blue{4}} \purple{\bigg)} }^{ - \blue{3}} } \orange{ \tt + { \purple{\bigg(}\frac{ \blue{1}}{\blue{13}} \purple{\bigg)} }^{ - \blue{1}} = \blue{126}}}}}$