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Question
The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is
Options
\[\frac{1}{2}\]
2
\[\frac{1}{4}\]
4
Solution
Find the value of `{8^ (- 4/3)÷ 2^-2}^(1/2)`
`{8^ (- 4/3)÷ 2^-2}^(1/2) = {2^(3x-4/3)÷2^-2 }^(1/2)`
`= {2^(3x(-4)/3)÷2^-2 }^(1/2)`
`= {2^-4 ÷2^-2 }^(1/2)`
`{8^ (- 4/3)÷ 2^-2}^(1/2) = {2^(-4xx1/2)÷ 2^(-2xx1/2)}`
`= {2^(-4xx1/2)÷ 2^(-2xx1/2)}`
` = {2^2 ÷ 2^-1}`
` = {(1/2^2)/(1/2)}`
`{8^ (- 4/3)÷ 2^-2}^(1/2) = {1/(2xx2) xx 2/1}`
=`{1/(2xx2) xx 2/1}`
= `1/2`
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