Find the value of

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., $a^{m} \times a^{n}=a^{m+n}$.

We have:

$\left(5 x^{6}\right) \times\left(-1.5 x^{2} y^{3}\right) \times\left(-12 x y^{2}\right)$

$=\{5 \times(-1.5) \times(-12)\} \times\left(x^{6} \times x^{2} \times x\right) \times\left(y^{3} \times y^{2}\right)$

$=\{5 \times(-1.5) \times(-12)\} \times\left(x^{6+2+1}\right) \times\left(y^{3+2}\right)$

$=90 x^{9} y^{5}$

$\therefore\left(5 x^{6}\right) \times\left(-1.5 x^{2} y^{3}\right) \times\left(-12 x y^{2}\right)=90 x^{9} y^{5}$

Substituting x = 1 and y = 0.5 in the result, we get:

$90 x^{9} y^{5}$

$=90(1)^{9}(0.5)^{5}$

$=90 \times 1 \times 0.03125$

$=2.8125$

Thus, the answer is 2.8125.