Math, asked by harsh1328, 1 year ago

simplify 4 upon 216 ki power minus 2 upon 3 + 1 upon 256 ki power minus 3 upon 4 + 2 upon 243 ki power minus 1 upon 5 please solve

Answers

Answered by rajivrtp
2

question

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

= (54)⅔ + (256)¾ + (243/2)¹/5

[ 54=3³×2;. 256= 4⁴ , 243= 3^5 ] therefore

= 9(2)⅔+ 4³+ 3(1/2)¹/5

= 64+ 9×2⅔+3×1/2¹/5

this is simplest form

Answered by Salmonpanna2022
1

 \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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