smc

$[{\log }_{10}(5{\log }_{10}100){]}^2$ Since $10^2=100$, we have ${\log }_{10}100=2$, so: $[{\log }_{10}(5\cdot 2){]}^2$ Multiply: $[{\log }_{10}(10){]}^2$ Since $10^1=10$, we have ${\log }_{10}10=1$, so: $[1{]}^2$ $1$ $\boxed{1}$.