Answer:
The expression is
⇒ 2nd answer
Step-by-step explanation:
* Lets explain how to solve the problem
- In the exponent rules, we add the exponents when we multiply terms
have same base
- Ex: ![a^{m}*a^{n}=a^{m+n}](https://tex.z-dn.net/?f=a%5E%7Bm%7D%2Aa%5E%7Bn%7D%3Da%5E%7Bm%2Bn%7D)
- The volume of the rectangular box is the product of its three
dimensions
* Lets solve the problem
- John buys a water tank from a company
- The tank he buys has the dimensions b² by b^4 by 4c³
∵ The water tank is shaped a rectangular box
∵ The tank has dimensions ![b^{2},b^{4},4c^{3}](https://tex.z-dn.net/?f=b%5E%7B2%7D%2Cb%5E%7B4%7D%2C4c%5E%7B3%7D)
∵ The volume of the tank = L × W × H , where L , W , H are the
dimensions of the tank
- Assume that L = b² , W =
and H = 4c³
∴ The volume of the tank = b² ×
× 4c³
- b² and b^4 has the same base, then add its exponents
∴ The volume of the tank =
× 4c³
∴ The volume of the tank =
× 4c³
∴ The volume of the tank = ![4b^{6}c^{3}](https://tex.z-dn.net/?f=4b%5E%7B6%7Dc%5E%7B3%7D)
* The expression which represents the volume of the tank is:
![4b^{6}c^{3}](https://tex.z-dn.net/?f=4b%5E%7B6%7Dc%5E%7B3%7D)
∴ The answer is the second expression