Express each of the following product as a monomials and verify the result for x = 1, y = 2:

Question:

Express each of the following product as a monomials and verify the result for x = 1, y = 2:

$\left(\frac{4}{9} a b c^{3}\right) \times\left(-\frac{27}{5} a^{3} b^{2}\right) \times\left(-8 b^{3} c\right)$

Solution:

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:

$\left(\frac{4}{9} a b c^{3}\right) \times\left(-\frac{27}{5} a^{3} b^{2}\right) \times\left(-8 b^{3} c\right)$

$=\left\{\left(\frac{4}{9}\right) \times\left(-\frac{27}{5}\right) \times(-8)\right\} \times\left(a \times a^{3}\right) \times\left(b \times b^{2} \times b^{3}\right) \times\left(c^{3} \times c\right)$

$=\left\{\left(\frac{4}{9}\right) \times\left(-\frac{27}{5}\right) \times(-8)\right\} \times\left(a^{1+3}\right) \times\left(b^{1+2+3}\right) \times\left(c^{3+1}\right)$

$=\frac{96}{5} a^{4} b^{6} c^{4}$

Thus, the answer is $\frac{96}{5} a^{4} b^{6} c^{4}$.

$\because$ The expression doesn't consist of the variables $x$ and $y$.

$\therefore$ The result cannot be verified for $x=1$ and $y=2$