Final answer:
The question involves solving the algebraic equation 4x+3=112+32x to find x, and then using that value to evaluate the expression (18x)^(3x) by applying the laws of exponents.
Step-by-step explanation:
The student is asking to solve an algebraic equation and then find the value of an expression involving the solution. The given equation is 4x+3=112+8×4x, which simplifies to 4x+3=112+32x. By solving this equation, we can find the value of x. Once we have the value of x, we can calculate the value of (18x)^(3x), which involves using the laws of exponents.
Firstly, we solve the equation:
4x + 3 = 112 + 32x
4x + 3 - 32x = 112
-28x + 3 = 112
-28x = 112 - 3
-28x = 109
x = 109 / -28
x = -109/28
Once we have the value of x, we then substitute it into the expression (18x)^(3x) and simplify.