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Quotient Law

Find value :-...

Question

Find value :-
$[[(256)^{- (4^{- 3 / 2})}]^{- 3} \div [4^{3} \div 2^{- 3}]^{- 1 / 3}]$ = ?

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Solution

$⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ {⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ (256)^{- ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ 4^{- \frac{3}{2}} ⎞ ⎟ ⎟ ⎟ ⎟ ⎠} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦}^{- 3} \div {[4^{3} \div 2^{- 3}]}^{\frac{- 1}{3}} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦$
$\Rightarrow {⎡ ⎢ ⎢ ⎢ ⎣ {[(16)^{2}]}^{- (2^{2})^{\frac{3}{2}}} ⎤ ⎥ ⎥ ⎥ ⎦}^{- 3} \div {[4^{3} \div \frac{1}{2^{3}}]}^{\frac{- 1}{3}}$
$\Rightarrow {[(4^{4})^{- (2^{- 3})}]}^{- 3} \div [4^{3} \times 2^{3}]^{\frac{- 1}{3}}$
$\Rightarrow {⎡ ⎢ ⎣ (4^{4})^{- \frac{1}{8}} ⎤ ⎥ ⎦}^{- 3} \div [4 \times 2]^{- 1}$
$\Rightarrow (4^{4})^{\frac{3}{8}} \times 8$
$\Rightarrow (4)^{\frac{3}{2}} \times 8 \Rightarrow 2^{3} \times 8 \Rightarrow 64$
$⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ {⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ (256)^{- ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ 4^{- \frac{3}{2}} ⎞ ⎟ ⎟ ⎟ ⎟ ⎠} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦}^{- 3} \div {[4^{3} \div 2^{- 3}]}^{\frac{- 1}{3}} ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ = 64$

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Similar questions

Q. Find the value of

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

Q. Find the value of :

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

Q. Find the value of

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

Q. Find the value of

\frac{4}{216^{\frac{- 2}{3}}}

\frac{1}{256^{\frac{- 3}{4}}}

\frac{2}{243^{\frac{- 1}{5}}}

Q. Question 7
Find the value of

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

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