Evaluate (2.3 a^5 b^2 ) (1.2 a^2 b^2 ) when a = 1 and b = 0.5. - Vidyadip

Question

Evaluate $ \left(2.3 a^5 b^2\right) \times\left(1.2 a^2 b^2\right) $ when $a = 1$ and $b = 0.5$.

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Answer

To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e. $a^m× a^n= a^{m+n}$.
$ \left(2.3 a^5 b^2\right) \times\left(1.2 a^2 b^2\right) $
$ =(2.3 \times 1.2) \times\left(a^5 \times a^2\right) \times\left(b^2 \times b^2\right) $
$ =(2.3 \times 1.2) \times\left(a^5+2\right) \times\left(b^2+2\right) $
$ =2.76 a^7 b^4 $
$ \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(1)^7(0.5)^4 $
$ =2.76 \times 1 \times 0.0625 $
$ =0.1725$
Thus, the answer is $= 0.1725$

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