Answer:
The expression is [tex]4b^{6}c^{3}[/tex] ⇒ 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: [tex]a^{m}*a^{n}=a^{m+n}[/tex]
- 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 [tex]b^{2},b^{4},4c^{3}[/tex]
∵ The volume of the tank = L × W × H , where L , W , H are the
dimensions of the tank
- Assume that L = b² , W = [tex]b^{4}[/tex] and H = 4c³
∴ The volume of the tank = b² × [tex]b^{4}[/tex] × 4c³
- b² and b^4 has the same base, then add its exponents
∴ The volume of the tank = [tex]b^{4+2}[/tex] × 4c³
∴ The volume of the tank = [tex]b^{6}[/tex] × 4c³
∴ The volume of the tank = [tex]4b^{6}c^{3}[/tex]
* The expression which represents the volume of the tank is:
[tex]4b^{6}c^{3}[/tex]
∴ The answer is the second expression
