Question

Find the value of (5x⁶) × (−1.5x²y³) × (−12xy²) when x = 1, y = 0.5.

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:

$$\begin{gathered} \left(5x^6\right)\times \left(-1.5x^2{y}^3\right)\times \left(-12x{y}^2\right) \\ =\left\{5\times \left(-1.5\right)\times \left(-12\right)\right\}\times \left(x^6\times x^2\times x\right)\times \left(y^3\times y^2\right) \\ =\left\{5\times \left(-1.5\right)\times \left(-12\right)\right\}\times \left(x^{6+2+1}\right)\times \left(y^{3+2}\right) \\ =90x^9{y}^5 \end{gathered}$$

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

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

$$\begin{gathered} 90x^9{y}^5 \\ =90{\left(1\right)}^9{\left(0.5\right)}^5 \\ =90\times 1\times 0.03125 \\ =2.8125 \end{gathered}$$

Thus, the answer is 2.8125.