Question

please solve it with full explanation and as fast as you can​

Answer 1

Answer:

Value of given expression is 214 .

Step-by-step explanation:

Given expression is;

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

Now as we know that $6^{3}$ = 216 , $4^{4}$ = 256 and $3^{5}$ = 243

Putting these in above expression we get;

              ⇒    $\frac{4}{(6^{3} )^{\frac{-2}{3} } } + \frac{1}{(4^{4} )^{\frac{-3}{4} } } + \frac{2}{(3^{5} )^{\frac{-1}{5} } }$

              ⇒     $\frac{4}{(6 )^{3*\frac{-2}{3} } } + \frac{1}{(4 )^{4*\frac{-3}{4} } } + \frac{2}{(3 )^{5*\frac{-1}{5} } }$

              ⇒    $\frac{4}{(6 )^{-2} } } + \frac{1}{(4 )^{-3} } } + \frac{2}{(3 )^{-1} } }$  

              ⇒    $4*(6 )^{2} + 1*(4 )^{3} + 2*(3 )^{1}$

              ⇒   (4 * 36) + (1 * 64) + (2 * 3)

              ⇒   144 + 64 + 6 = 214 .

Therefore, value of given expression is 214 .