Question

[ ( \frac { 1 } { 3 } ) ^ { - 2 } - ( \frac { 1 } { 2} ) ^ { - 3 } ] \div [ \frac { 1 } { 4 } ] ^ { - 2 }​

Answer 1

Given Expression,

$\sf[ ( \dfrac { 1 } { 3 } ) ^ { - 2 } - ( \dfrac { 1 } { 2} ) ^ { - 3 } ] \div [ \dfrac { 1 } { 4 } ] ^ { - 2 }$

Now Simplify,

$\sf \bigg[ \bigg( {\dfrac {1 } { 3 } \bigg) }^{ - 2} - \bigg ( \dfrac { 1 } { 2} \bigg) ^ { - 3 } \bigg ] \div \bigg [ \dfrac { 1 } { 4 } \bigg ] ^ { - 2 }$

$\sf \bigg \lgroup \: {(3) }^{2} - {( - 2)}^{3} \bigg \rgroup \div {(4)}^{2}$

$\red{\therefore a^n=\dfrac{1}{a^{-9}}}$

$\sf \: =[9-8]÷16$

$\sf \: =1÷16$

$\sf \bigg( \: \dfrac{1}{16} \bigg)$

Hence the answer is

$\red{ \star\boxed{ \underline{ \sf \bigg( \: \dfrac{1}{16} \bigg)}}}$