Question

The mass of an armored tank is $6\times {10}^4\text{kg}$ and of an armored car is $4\times {10}^3\text{kg}.$ What is the combined weight of both the vehicles?

• A. ${10}^5\text{kg}$
• B. $6.4\times {10}^5\text{kg}$
• C. $4.6\times {10}^4\text{kg}$
• D. $6.4\times {10}^4\text{kg}$

Answer 1

The correct option is D $6.4\times {10}^4\text{kg}$

$\text{Combined weight}=\left(\right(6\times {10}^4)+(4\times {10}^3\left)\right)\text{kg}$
But, $(6\times {10}^4)+(4\times {10}^3)=(6\times {10}^{3+1})+(4\times {10}^3)=(6\times {10}^1\times {10}^3)+(4\times {10}^3)(\because a^m\times a^n=a^{m+n})=(60\times {10}^3)+(4\times {10}^3)=64\times {10}^3=6.4\times 10\times {10}^3=6.4\times {10}^4$
Thus, the combined weight of the tank and the car is $6.4\times {10}^4\text{kg}$