The value of `"{"8^(-4/3)-:2^(-2)")"^(1/2)` is (a)`1/2` (b) 2 (c) `1/4` (d) 4

Explanation

Given:
`{8^(−4/3)÷2^(−2)}^(1/2)`
`=[(2^3)^(−4/3)÷2^(−2)]^(1/2)`
`=[2^(3×(−4/3))÷2^(−2)]^(1/2)`[Since, `(a^m)^n=a^(m×n)`]
`=[2^(3×−4/3)÷2^(−2)]^(1/2)`
`=[2^(−4)/2^(−2)]^(1/2)`
`=(2^(−4−(−2)))^(1/2)` [since, `a^m/a^n=a^(m−n), a!=0`]
`=(2^(−2))^(1/2)`
`=(1/2^2)^(1/2)`[Since, `a^(−m)=1/a^m`]
`=1/2^(2×1/2)=1/2`
`therefore {8^(−4/3)÷2^(−2)}^(1/2)=1/2`