Here Total no. of $0$'s to the right of each $1$'s should be even. So, to the left side of every $1$'s no. of $0$'s can be anything.
$L=\{ \epsilon ,0,00,000,01,011,0111,1,11,111,1111,100,10000,100100,10010000...................\}$
Hence,
$\mathbf{R.E.=0^*(1+00)^*= 0^*(1(00)^*)^* = 0^*(1+(00)^*)^* =0^*(1^*+(00))^* = 0^*(1^*+(00)^*)^*}$