Question

If `3^(4x) = (81)^-1` and `10^(1/y)=0.0001,` find the value of `  2^(-x+4y)`.

Answer 1

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`.