# If 34x = (81)-1 and (10)1/y

Question:

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

Solution:

$3^{4 x}=(81)^{-1}$ and $(10)^{1 / y}=0.0001$

$3^{4 x}=(3)^{-4}$

x = -1

And, $(10)^{1 / y}=0.0001$

$(10)^{1 / y}=(10)^{-4}$

$1 / y=-4$

$y=1 /-4$