To solve the expression \(40^2 \cdot 1.5(10 + 60)\), follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).
Calculate \(40^2\): \[ 40^2 = 1600 \]
Calculate the expression inside the parentheses: \[ 10 + 60 = 70 \]
Now substitute back into the expression: \[ 1600 \cdot 1.5 \cdot 70 \]
Calculate \(1.5 \cdot 70\): \[ 1.5 \cdot 70 = 105 \]
Finally, multiply \(1600 \cdot 105\): \[ 1600 \cdot 105 = 168000 \]
So, the final result is: \[ \boxed{168000} \]