Question

Evaluate (2.3a⁵b²) × (1.2a²b²) when a = 1 and b = 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:

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

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

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

$$\begin{gathered} 2.76a^7{b}^4 \\ =2.76{\left(1\right)}^7{\left(0.5\right)}^4 \\ =2.76\times 1\times 0.0625 \\ =0.1725 \end{gathered}$$

Thus, the answer is $0.1725$.