Question

If the side lengths of a cube are 14 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?
143
314
14 ⋅ 3
14 ⋅ 14 ⋅ 14
PLEASE ANWSER !!!!!
(100 points given)

Answer 1

Answer: Choice A) $14^3$

This is the same as writing 14^3

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Explanation:

Since all the sides are 14 feet long, we can basically say length = width = height = 14.

Or put another way:

• length = 14
• width = 14
• height = 14

The volume of the cube is length*width*height = 14*14*14 = 14^3 = 2744 cubic feet.

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The term 14^3 has a base of 14 and exponent of 3.

The base is what we multiply out while the exponent tells us how many copies of the base to multiply. In this problem, we have 3 copies of 14 being multiplied. So that's why 14^3 = 14*14*14

If you were to say something like 3^14, then you would have 14 copies of 3 multiplied out, which is a much larger value. So we'll cross choice B off the list.

Choice C isn't correct either since again we're using exponents and not multiplication to tie together the 14 and 3.

Choice D would be correct if your teacher wanted it in expanded form, instead of exponent form.