Math, asked by Sergeytvyt, 18 days ago

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Answered by mathdude500
3

Question:- Simplify and evaluate using law of exponents :

\rm \: [ {3}^{ - 9} \times  {3}^{2}] \div  {3}^{5}  \\

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

Given expression is

\rm \: [ {3}^{ - 9} \times  {3}^{2}] \div  {3}^{5}  \\

We know

\boxed{ \rm{ \: {a}^{m} \times  {a}^{n} =  {a}^{m + n} \: }} \\

So, using this law of exponents, we get

\rm \:  =  \:  {3}^{ - 9 + 2} \div  {3}^{5}  \\

\rm \:  =  \:  {3}^{ - 7} \div  {3}^{5}  \\

Now, we know that

\boxed{ \rm{ \: {a}^{m}  \div   {a}^{n} =  {a}^{m  -  n} \: }} \\

So, using this law of exponents, we get

\rm \:  =  \:  {3}^{ - 7 - 5}  \\

\rm \:  =  \:  {3}^{ - 12}  \\

Hence,

\rm\implies \:\boxed{ \rm{ \:\rm \: [ {3}^{ - 9} \times  {3}^{2}] \div  {3}^{5}  =  {3}^{ - 12}  \:  \: }} \\

\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}

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