Question

plz explain step by step ​

Answer 1

Answer:

24/5

Step-by-step explanation:

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Answer 2

Question :-

Simplify :

$\rm \: {\bigg( {2}^{ - 1} + {3}^{ - 1} \bigg) }^{ - 1} \div {4}^{ - 1}$

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm \: {\bigg( {2}^{ - 1} + {3}^{ - 1} \bigg) }^{ - 1} \div {4}^{ - 1}$

We know,

$\boxed{ \rm{ \: {x}^{ - n} \: = \: \frac{1}{ {x}^{n} } \: }}$

So, using this result, we get

$\rm \: = \: {\bigg(\dfrac{1}{2} + \dfrac{1}{3} \bigg) }^{ - 1} \div \dfrac{1}{4}$

$\rm \: = \: {\bigg(\dfrac{3 + 2}{6} \bigg) }^{ - 1} \times 4$

$\rm \: = \: {\bigg(\dfrac{5}{6} \bigg) }^{ - 1} \times 4$

We know,

$\boxed{ \rm{ \: {\bigg[\dfrac{x}{y} \bigg]}^{ - n} = {\bigg[\dfrac{y}{x} \bigg]}^{n} \: }}$

So, using this identity, we get

$\rm \: = \: \dfrac{6}{5} \times 4$

$\rm \: = \: \dfrac{24}{5}$

Hence,

$\color{green}\rm\implies \:\boxed{ \rm{ \: {\bigg( {2}^{ - 1} + {3}^{ - 1} \bigg) }^{ - 1} \div {4}^{ - 1} = \frac{24}{5} \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{ {x}^{0} = 1}\\ \\ \bigstar \: \bf{ {x}^{m} \times {x}^{n} = {x}^{m + n} }\\ \\ \bigstar \: \bf{ {( {x}^{m})}^{n} = {x}^{mn} }\\ \\\bigstar \: \bf{ {x}^{m} \div {x}^{n} = {x}^{m - n} }\\ \\ \bigstar \: \bf{ {x}^{ - n} = \dfrac{1}{ {x}^{n} } }\\ \\\bigstar \: \bf{ {\bigg(\dfrac{a}{b} \bigg) }^{ - n} = {\bigg(\dfrac{b}{a} \bigg) }^{n} }\\ \\\bigstar \: \bf{ {x}^{m} = {x}^{n}\rm\implies \:m = n }\\ \\ \end{array} }}\end{gathered}\end{gathered}\end{gathered}$