Final answer:
To solve for the value of B, we need to simplify the equation and compare the coefficients on both sides. The coefficient of B can be determined by equating the corresponding coefficients on both sides of the equation. In this case, B = 49.
Step-by-step explanation:
To solve for the value of B, we need to simplify the equation and compare the coefficients on both sides. Let's start by expanding the left side of the equation using the binomial theorem: (7x³ + y³/4)² = (7x³)² + 2(7x³)(y³/4) + (y³/4)².
Simplifying this further, we get: 49x⁶ + 49x³y³/2 + y⁶/16.
Now we can compare the coefficients: Bx⁶y^3/2 = Bx⁶ * y³/2.
Since Bx⁶y^3/2 = 49x⁶ + 49x³y³/2 + y⁶/16, we can equate the corresponding coefficients: B = 49.