What would happen to the cycling of nutrients, including water, oxygen and carbon dioxide, if plants died out on Earth?

Water would become less used and more abundant, oxygen would be less produced, and carbon dioxide would become more abundant because the plants won't take it in to produce glucose.

the overall balanced equation

6co2 + 6h2o > c6h12o6 + 6o2

sunlight energy

where: co2 = carbon dioxide

h2o = water

light energy is required

c6h12o6 = glucose

o2 = oxygen