The volume of a cube is given by the formula V = s3, where s is the length of one side. What is the volume of the cube including the planet? First, justify your answer using the Product of Powers Property. Then justify your answer using the Power of a Product Property.

1000 cm³

Explanation:

The product of powers property is a rule that helps in simplifying the difficulties that comes with multiplying powers of numbers. It states that when multiplying two powers having the same base, we take one of the base, and then just add the exponents.

This is illustrated in the example.

S¹ * S². The product of powers asks us to pick one of the bases, S, and then add up the powers, thus

S¹ * S² = S^(¹+²)

S¹ * S² = S³

Now, using this in our question, volume of the cube is S³. Since we aren't given a length, I'm going to assume a length.

L = 10 cm. We all know that all sides are equal in a cube,

So, S = 10 cm.

S³ = volume of the cube

V = 10³

V = 1000 cm³

Now, to test the property of products, we say

S = 10, even though it doesn't show any visible exponent, we know that it's raised to the power of 1, and thus

S = 10¹

V = S * S * S

V = 10¹ * 10¹ * 10¹

V = 10^(¹+¹+¹)

V = 10³

V = 1000 cm³

Justified

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