To simplify the left side of the equation, let's expand the expression first using the binomial theorem:

(sqrta + sqrtb)^8 = C(8,0)(sqrta)^8(sqrtb)^0 + C(8,1)(sqrta)^7(sqrtb)^1 + C(8,2)(sqrta)^6(sqrtb)^2 + C(8,3)(sqrta)^5(sqrtb)^3 + C(8,4)(sqrta)^4(sqrtb)^4 + C(8,5)(sqrta)^3(sqrtb)^5 + C(8,6)(sqrta)^2(sqrtb)^6 + C(8,7)(sqrta)^1(sqrtb)^7 + C(8,8)(sqrta)^0(sqrtb)^8

Now, substitute the values into the expanded expression:

= 1(a^4) + 8(a^3b^1) + 28(a^2b^2) + 56(a^1b^3) + 70(a^0b^4) + 56(a^1b^3) + 28(a^2b^2) + 8(a^3b^1) + 1(b^4)
= a^4 + 8a^3b + 28a^2b^2 + 56ab^3 + 70b^4 + 56ab^3 + 28a^2b^2 + 8a^3b + b^4

Now, let's simplify the right side of the equation:

16ab(a+b)^2
= 16ab(a^2 + 2ab + b^2)
= 16ab(a^2 + 2ab + b^2)
= 16a^3b + 32a^2b^2 + 16ab^3

Since we want to show that the left side of the equation is equal to the right side of the equation, we want to show that:

a^4 + 8a^3b + 28a^2b^2 + 56ab^3 + 70b^4 + 56ab^3 + 28a^2b^2 + 8a^3b + b^4 = 16a^3b + 32a^2b^2 + 16ab^3

From the expanded expression of the left side, we can see that it simplifies to be equal to the right side of the equation; therefore, we have shown that:

(sqrta + sqrtb)^8 = 16ab(a+b)^2