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Question
If `3^(4x) = (81)^-1` and `10^(1/y)=0.0001,` find the value of ` 2^(-x+4y)`.
Solution
It is given that `3^(4x) = (81)^-1` and `10^(1/y)=0.0001`
Now,
`3^(4x) = (81)^-1`
`rArr3^(4x)=(3^4)^(-1)`
`rArr(3^x)^4=(3^-1)^4`
`rArrx=-1`
And,
`10^(1/y)=0.0001`
`rArr10^(1/y)=1/10000`
`rArr10^(1/y)=(1/10)^4`
`rArr10^(1/y)=(10)^-4`
`rArr1/y=-4`
`rArry=-1/4`
Therefore, the value of `2^(-x+4y)` is `2^(1+4(-1/4))=2^0=1`.
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