Powers and roots

let me solve without expression so that u better understand it.

400^300 = (20*20)^300 = 20^(2*300) = 20^600

Now add two 20^600 and divide by 2
you will again get 20^600

so final equn is
(20^600)^4
= (20)^(600*4) = 20^2400
= 20^(2*1200)
= 400^1200 [as 20^2 = 400]

Rules you need to remember

(A^b)^c = A^(b*c)
A^a * A^b = A^(a+b)

simplify
( 1/2 * (400^300 + 20^ 600) )^4 = 400^k
( 1/2 * (20^600 + 20^ 600) )^4 = 20^2k
( 1/2 * 2*20^600 )^4 = 20^2k
20^2400 = 20^2k
2400 = 2k
k = 1200

D