Question

pls answer iwant the ANSWER

Answer 1

Answer:

few identities which can be used is :

a to the power -1 = 1/a

$\frac{{x}^{a}}{ {x}^{b} } = {x}^{a - b}$

Answer 2

Answer:-

$\sf \large{ 1. \: [({4)}^{ - 1} - {(5)}^{ - 1}] ^{ - 1} \div {[( {5}^{2}) }^{3} \times {5}^{ - 5} ]}$

Using a^(- n) = 1/a^n and (a^m)^n = a^(mn) we get,

$\sf \implies \: \frac{1}{ {4}^{ - 1} - {5}^{ - 1} } \div {5}^{6} \times {5}^{ - 5}$

$\sf \implies \: \frac{1}{ \frac{1}{4} - \frac{1}{5} } \div {5}^{6 - 5}$

[Since, a^m × a^n = a^(m + n)]

$\sf \implies \: \frac{1}{ \frac{5 - 4}{20} } \div {5}^{1}$

$\sf \implies \: \frac{20}{1} \div 5$

$\implies \sf \large\red{{4}}$

$\sf \large{2. \: [{( \frac{1}{4} )}^{ - 1} + { (\frac{1}{3} )}^{ - 2} - ( { \frac{1}{2} )}^{ - 3} ] \div {5}^{2} }$

$\sf \implies \: {( {4}^{ - 1} )}^{ - 1} + { ({3}^{ - 1} )}^{ - 2} - {( {2}^{ - 1} )}^{ - 3} \div {5}^{2}$

$\sf \implies \: (4 + {3}^{2} - {2}^{3} ) \div {5}^{2}$

$\sf \implies \: (4 + 9 - 8) \div {5}^{2}$

$\sf \implies \: \frac{5}{25}$

$\implies \sf \large{ \red{\frac{1}{5} }}$