Write down the product of −8x2y6 and −20xy. Verify the product for x = 2.5, y = 1.
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:
$\left(-8 x^{2} y^{6}\right) \times(-20 x y)$
$=\{(-8) \times(-20)\} \times\left(x^{2} \times x\right) \times\left(y^{6} \times y\right)$
$=\{(-8) \times(-20)\} \times\left(x^{2+1}\right) \times\left(y^{6+1}\right)$
$=-160 x^{3} y^{7}$
$\therefore\left(-8 x^{2} y^{6}\right) \times(-20 x y)=-160 x^{3} y^{7}$
Substituting x = 2.5 and y = 1 in LHS, we get:
$\mathrm{LHS}=\left(-8 x^{2} y^{6}\right) \times(-20 x y)$
$=\left\{-8(2.5)^{2}(1)^{6}\right\} \times\{-20(2.5)(1)\}$
$=\{-8(6.25)(1)\} \times\{-20(2.5)(1)\}$
$=(-50) \times(-50)$
$=2500$
Substituting x = 2.5 and y = 1 in RHS, we get:
$\mathrm{RHS}=-160 x^{3} y^{7}$
$=-160(2.5)^{3}(1)^{7}$
$=-160(15.625) \times 1$
$=-2500$
Because LHS is equal to RHS, the result is correct.
Thus, the answer is $-160 x^{3} y^{7}$.
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