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प्रश्न
Simplify and express with a positive index.
`root(4)(81a^12b^-16)`
सोपे रूप द्या
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उत्तर
Given,
`root(4)(81a^12b^-16)`
We need to simplify and express with a positive index the given terms.
Thus, `root(4)(81a^12b^-16)`
= `root(4)(3^4a^12b^-16)`
= `(3^4a^12b^-16)^(1/4)` ...`[∴ root(n)(a) = a^(1/n)]`
The power `1/4` is taken for each factor inside the bracket.
= `(3^4)^(1/4) xx (a^12)^(1/4) xx (b^-16)^(1/4)`
= `3^(4 xx 1/4) xx a^(12 xx 1/4) xx b^(-16 xx 1/4)` ...[(am)n = amn]
= `3^1 xx a^3 xx b^-4`
= `(3a^3)/b^4` ...`[∴ a^-n = 1/a^n]`
Hence, `root(4)(81a^12b^-16) = (3a^3)/b^4`.
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