Answer: Therefore, (10ab)^2(2a^4b^3)/4a^5b simplifies to 50a^6b^4.
Step-by-step explanation: To simplify the expression, we can first expand the square of (10ab)^2, which gives us:
(10ab)^2 = 10^2 * a^2 * b^2 = 100a^2b^2
Substituting this into the expression gives:
(100a^2b^2)(2a^4b^3)/4a^5b
Simplifying the numerical factors, we get:
(50a^2b^2)(a^4b^3)/a^5b
Now we can cancel out common factors in the numerator and denominator:
(50)(a^2)(b^2)(a^4)(b^3)/(a^5)(b)
= (50a^2b^2)(a^4b^2)
= 50a^6b^4
Therefore, (10ab)^2(2a^4b^3)/4a^5b simplifies to 50a^6b^4.