What does it mean to be cubed? Start with visualizing a cube . We know that a cube has 3 dimensions: length, width and height and all three are the same length. To find the volume of a cube we multiply length times width times height. If we let x represent the side length we can write the formula V = x³ which means the volume is x •x •x . Cubed means to multiply a number by itself 3 times.



Let's practice with numbers.

Example 1: 4³ = 4 •4 •4 = 64

Let's practice evaluating with variables.

Example 2: find x³ if x = 5.

Substitute (5) in for x. x³ = (5)³

Expand x³ = 5 •5 •5 = 125

Therefore x³ = 125

Let's look at a common mistake.

Remember that x³ = x •x •x so what does - x³ represent? It means (-1) •x •x •x

Example 3: find - x³ when x = 1

Substitute (1) in for x. -x³ = - (1)x³

Expand -x³= -1 •1 •1 •1 = -1

Therefore -x³ = -1

Challenge: find 3 x² y³ when x = 4 and y = 3

Substitute (4) for x and (3) for y 3 x² y³ = 3 • (4)² • (3)³

Expand      3 x² y³ = 3 •(4) •(4) •(3) •(3) •(3)

3 x² y³ = 1296

Let's sum this up. Remember that to be "cubed" means to multiply a number times itself three times.

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