The combined volume of two identical cubes is 128 cubic centimeters. What is the side length of each cube

Firstly, let's make a diagram that suitable for the information above. Notice that we have two identical cubes. Therefore, we divide the volume of two cubes into two equal parts to prepare the volume of one cube.

[tex]\boxed{64 \ cm^3}\boxed{64 \ cm^3} = 128 \ cm^3 \ or \ \boxed{ \ 128 \ cm^3 \div 2 = 64 \ cm^3 \ }[/tex]

Hence, the volume of a cube is 64 cm³.

Secondly, we will find out the side length of each cube.

In a cube, all the sides are the same.

Recall the volume of a cube is [tex]\boxed{ \ V = s \times s \times s \ or \ V = s^3 \ }[/tex], where s is the length of one side of the cube.

Let us calculate the side length of each cube.

[tex]\boxed{ \ s \times s \times s \ = 64 \ }[/tex]

The diagram that satisfies this equation is as follows:

[tex]\boxed{4}\boxed{4}\boxed{4} = 64[/tex]

[tex]Since \ \boxed{64 \div 4 = 16} \ and \ \boxed{16 \div 4 = 4}, hence \ \boxed{4 \times 4 \times 4 = 64}[/tex]

Thus, the side length of each cube is 4 cm.

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