# Evaluate Cubes

**? 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 = x**

*cubed*^{3}which means the volume is x •x •x . Cubed means to multiply a number by itself 3 times.

^{3}=x •x •x

Let's practice with numbers.

Example 1: 4

^{3}= 4 •4 •4 = 64

Let's practice evaluating with variables.

Example 2: find x

^{3}if x = 5.

Substitute (5) in for x.

^{3}= (5)

^{3}

Expand

^{3}= 5 •5 •5 = 125

Therefore

^{3}= 125

Let's look at a

*common mistake*.

Remember that x

^{3}= x •x •x so what does - x

^{3}represent? It means (-1) •x •x •x

Example 3: find - x

^{3}when x = 1

Substitute (1) in for x.

^{3}= - (1)x

^{3}

Expand

^{3}= -1 •1 •1 •1 = -1

Therefore

^{3}= -1

Challenge: find 3 x

^{2}y

^{3}when x = 4 and y = 3

Substitute (4) for x and (3) for y

^{2}y

^{3}= 3 • (4)

^{2}• (3)

^{3}

Expand

^{2}y

^{3}= 3 •(4) •(4) •(3) •(3) •(3)

^{2}y

^{3}= 1296

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

Related Links:Math algebra Evaluate Exponents |

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