A larger reactor is needed to replace the existing smaller, $100-$gallon $300$ psi reactor currently in use in the quantum physics lab. If the original reactor has a cost of $$15,750,$ what is the cost of a reactor that is $75\%$ larger, assuming a power$-$sizing exponent of $0\mathrm{.}56?$

$$27563$

$$21547$

$$11512$

$$17846$