what expression raised to the fourth power is 81?
x with exponent 12
y with exponent 8
z with exponent 12
that is nothing like the original equation, even some of the powers are different and there is no z, make sure you're not making a typo.
do you mean $\displaystyle 81x^{12} y^8 z^{16}$?
if so, the answer is $\displaystyle 3 x^3 y^2 z^4$
when we raise products to a power, we multiply the powers by the power we are raising to, that is, $\displaystyle (xy)^n = x^n y^n$. with that knowledge in mind, we simply take out a factor of four from the powers of all the expressions, since if we raise this new expression to the power four, we would multiply all the powers by 4 and get back the expression we started with