Evaluate

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:

$\left(2.3 a^{5} b^{2}\right) \times\left(1.2 a^{2} b^{2}\right)$

$=(2.3 \times 1.2) \times\left(a^{5} \times a^{2}\right) \times\left(b^{2} \times b^{2}\right)$

$=(2.3 \times 1.2) \times\left(a^{5+2}\right) \times\left(b^{2+2}\right)$

$=2.76 a^{7} b^{4}$

$\therefore\left(2.3 a^{5} b^{2}\right) \times\left(1.2 a^{2} b^{2}\right)=2.76 a^{7} b^{4}$

Substituting a =1 and b = 0.5 in the result, we get:

$2.76 a^{7} b^{4}$

$=2.76(1)^{7}(0.5)^{4}$

$=2.76 \times 1 \times 0.0625$

$=0.1725$

Thus, the answer is $0.1725$.