Math, asked by lingadallisuresh01, 7 months ago

simplify 4/(216)^-2/3+1/256^-3/4+2/(243)^-1/5​

Answers

Answered by izaan2007
1

Answer:

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Answered by Salmonpanna2022
2

Step-by-step explanation:

 \bf \underline{Evaluate-} \\

 \sf\:  \dfrac{4}{ ({216)^{ \frac{ - 2}{3}  } } }  +  \dfrac{1}{ ({256)^{ \frac{ - 3}{4}  } } }  +  \dfrac{2}{ ({243)^{ \frac{ - 1}{5}  } } }

 \bf \underline{Solution-} \\

\sf \:  \:  \implies \: \:  \dfrac{4}{ ({216)^{ \frac{ - 2}{3}  } } }  +  \dfrac{1}{ ({256)^{ \frac{ - 3}{4}  } } }  +  \dfrac{2}{ ({243)^{ \frac{ - 1}{5}  } } }

\sf \:  \:  \implies \: \:  \dfrac{4}{ ({6 \times 6 \times 6)^{ \frac{ - 2}{3}  } } }  +  \dfrac{1}{ ({4 \times 4 \times 4  \times 4)^{ \frac{ - 3}{4}  } } }  +  \dfrac{2}{ ({3 \times 3 \times 3 \times 3 \times 3)^{ \frac{ - 1}{5}  } } }

\sf \:  \:  \implies \: \:  \dfrac{4}{ ({ {6}^{3} )^{ \frac{ - 2}{3}  } } }  +  \dfrac{1}{ ({ {4}^{4} )^{ \frac{ - 3}{4}  } } }  +  \dfrac{2}{ ({ {3}^{5} )^{ \frac{ - 1}{5}  } } }

\sf \:  \:  \implies \: \:  \dfrac{4}{ ({ {6} )^{3 \times  \frac{ - 2}{3}  } } }  +  \dfrac{1}{ ({ {4} )^{ 4 \times \frac{ - 3}{4}  } } }  +  \dfrac{2}{ ({ {3})^{5 \times  \frac{ - 1}{5}  } } }

\sf \:  \:  \implies \: \:  \dfrac{4}{ ({ {6} )^{ - 2  } } }  +  \dfrac{1}{ ({ {4} )^{  - 3  } } }  +  \dfrac{2}{ ({ {3})^{ - 1 } } }

\sf \:  \:  \implies \: \:  \dfrac{4}{ {   \dfrac{1}{ {6}^{2} }   } }  +  \dfrac{1}{ {   \dfrac{1}{ {4}^{3} }   } }  +  \dfrac{2}{ {  \dfrac{1}{3}  } }

\sf \:  \:  \implies \: \:  \dfrac{4}{ {   \dfrac{1}{ 36}  } }  +  \dfrac{1}{ {   \dfrac{1}{ 64 }   } }  +  \dfrac{2}{ {  \dfrac{1}{3}  } }

\sf \:  \:  \implies \: \:  4 \times 36 +  64  +  2 \times 3

\sf \:  \:  \implies \: \:  144 +  64  +  6

\sf \:  \:  \implies \: \:  144 +  70

\bf \:  \:  \implies \: \:  214\\

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