a^b=27
and, a*(b)^2 = 8
so, what is the value of a and b ?
I graphed both these equations and the intersection is where they are both true.
The approximate solution from the graph is a=0.4555 and b= -4.191
Let's see how close this is
0.4555^-4.191 = 26.9944941684914683 rounded of to 1 dp = 27.0
0.4555*(-4.191)^2 = 8.0006210955 rounded of to 1 dp = 8.0
That is pretty close :)
Here is the graph that I used.