Question

Evaluate (−8x²y⁶) × (−20xy) for x = 2.5 and y = 1.

Answer 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:

$$\begin{gathered} \left(-8x^2{y}^6\right)\times \left(-20xy\right) \\ =\left\{\left(-8\right)\times \left(-20\right)\right\}\times \left(x^2\times x\right)\times \left(y^6\times y\right) \\ =\left\{\left(-8\right)\times \left(-20\right)\right\}\times \left(x^{2+1}\right)\times \left(y^{6+1}\right) \\ =160x^3{y}^7 \end{gathered}$$

$\therefore$ $\left(-8x^2{y}^6\right)\times \left(-20xy\right)=160x^3{y}^7$

Substituting x = 2.5 and y = 1 in the result, we get:

$$\begin{gathered} 160x^3{y}^7 \\ =160{\left(2.5\right)}^3{\left(1\right)}^7 \\ =160\times 15.625 \\ =2500 \end{gathered}$$

Thus, the answer is $2500$.