Math, asked by kartikarora1234qw, 1 month ago

simplify and write it in exponential form with negative exponent 2^{-1}[(\frac{5}{3})^{4}+(\frac{3}{5})^{-2}]\div\frac{17}{9}​

Answers

Answered by DIPanJaN4422
1

Step-by-step explanation:

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Answered by AestheticSky
37

  \maltese \: \large  \underbrace\orange{ \pmb{ \frak{Proper \:  Question : -  }}}

  • Simplify and write it in exponential form with negative exponent.

    :  \implies \sf 2^{-1} \bigg[  \bigg(\dfrac{5}{3} \bigg)^{4}+ \bigg(\dfrac{3}{5} \bigg)^{-2} \bigg]\div\dfrac{17}{9} \\

\maltese \: \large  \underbrace\orange{ \pmb{ \frak{Solution: -  }}}

 \\   :  \implies \sf 2^{-1} \bigg[  \bigg(\dfrac{5}{3} \bigg)^{4}+ \bigg(\dfrac{3}{5} \bigg)^{-2} \bigg]\div\dfrac{17}{9} \\

We know that :-

 \\  \leadsto \underline{ \boxed{ \pink{{ \sf{ \bigg( \frac{a}{b}  \bigg)  ^{ - c} =  \bigg( \frac{b}{a}  \bigg) ^{c}  }}}}} \bigstar \\

Applying the same concept here, we'll get :-

 \\   : \implies \dfrac{1}{2}  \bigg[  \bigg(\dfrac{5}{3} \bigg)^{4}+ \bigg(\dfrac{5}{3} \bigg)^{2} \bigg]\div\dfrac{17}{9} \\

 \\   : \implies \dfrac{1}{2}  \bigg[  \bigg(\dfrac{625}{81} \bigg)+ \bigg(\dfrac{25}{9} \bigg) \bigg]\div\dfrac{17}{9} \\

 \\   : \implies\dfrac{1}{2} \times   \dfrac{835}{ 81}  \times \dfrac{ 9}{17} \\

 \\   : \implies \sf \dfrac{25}{9}  =  \bigg( \frac{5}{3}  \bigg)  ^{2}  \\

  \\ :   \implies   \underline{\boxed  {\pink{{ \frak{  \bigg(\frac{3}{5}  \bigg)  ^{ - 2}  }}}}} \bigstar \\

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