If $p,q$ are positive quantities and $0 \leq m\leq 1$ then Prove that $$(p+q)^m \leq p^m+q^m$$
Trial: For $m=0$, $(p+q)^0=1 < 2= p^0+q^0$
and for $m=1$, $(p+q)^1=p+q =p^1+q^1$.
So, For $m=0,1$ the inequality is true.How I show that the inequality is also true for $0 < m < 1$.
Please help.