plotting - Visualize Plot of a function of 3 Variables using color and contours

I would like to plot a function of three variables, say for example:

$$f(x,y,z) = x^2+y^3+z^4$$

over $[-1, +1]$. I want my plot to use colors and maybe contours to make this visualization possible using a single plot. Any ideas? Example code would help a lot!

EDIT

I would like to have the $xy$ axes shown and $z$ as a "dynamic" variable (with sliding bar) and the output as a flat, colored contour map.

Answer

Manipulate[
     ContourPlot[x^2 + y^3 + z^4, {x, -1, 1}, {y, -1, 1}, ColorFunction -> "DarkRainbow"]
,{z, -1, 1}]

enter image description here

EDIT:

A few values in 3D plot:

Plot3D[Evaluate@Table[x^2 + y^3 + z^4, {z, {0, 0.8, 1}}], {x, -1, 1}, {y, -1, 1}, PlotStyle -> {Red, Green, Blue}]

enter image description here

But I'd rather put a few contour plots next to each other. In general take a look at the Mathematica help, there are lots of examples. You'll also find more options, like ColorFunctionScaling

 With[{z = 0}, 
  ContourPlot[x^2 + y^3 + z^4, {x, -1, 1}, {y, -1, 1}, 
  ColorFunction -> "DarkRainbow", 
  PlotLegends -> BarLegend[Automatic]]
 ]

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