what is the equilibrium expression for

P4(s) +5O2(g)<====>P4O10(s)

I think it is 1/[O2]^5
but the answer says [P4010]/[P4][O2]^5

You are right (for Kc). The answer is wrong.

To determine the equilibrium expression for a given reaction, you need to write the expression using the concentrations of the products and reactants raised to their stoichiometric coefficients. In this case, the stoichiometric coefficients for the reaction P4(s) + 5O2(g) ⇌ P4O10(s) are 1 and 5, respectively.

The equilibrium expression can be written as [products]/[reactants], where the concentrations are raised to their stoichiometric coefficients.

Therefore, the correct equilibrium expression for this reaction is [P4O10] / [P4][O2]^5. The concentration of P4O10 is divided by the product of the concentrations of P4 raised to the power of one and O2 raised to the power of five.

So, the answer you provided, [P4O10] / [P4][O2]^5, is the correct equilibrium expression for the given reaction.