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:

\[\left( 2 . 3 a^5 b^2 \right) \times \left( 1 . 2 a^2 b^2 \right)\]

\[ = \left( 2 . 3 \times 1 . 2 \right) \times \left( a^5 \times a^2 \right) \times \left( b^2 \times b^2 \right)\]

\[ = \left( 2 . 3 \times 1 . 2 \right) \times \left( a^{5 + 2} \right) \times \left( b^{2 + 2} \right)\]

\[ = 2 . 76 a^7 b^4\]

\[\therefore\] \[\left( 2 . 3 a^5 b^2 \right) \times \left( 1 . 2 a^2 b^2 \right) = 2 . 76 a^7 b^4\]

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

\[2 . 76 a^7 b^4 \]

\[ = 2 . 76 \left( 1 \right)^7 \left( 0 . 5 \right)^4 \]

\[ = 2 . 76 \times 1 \times 0 . 0625\]

\[ = 0 . 1725\]

Thus, the answer is \[0 . 1725\].