Question

Bellwork A cube has side lengths of 6 units. Write an integer expression to express the volume of the cube.. A square garden has side lengths of 10 units.

Write an integer expression to express the area of the square.
What if you had 2 cubes both with side lengths of 7 units, write an exponential integer for each cube and then multiply the two expressions.
Explain the steps that you would take to find the product of the two volumes.

Answer 1

The volume of a cube with side lengths of 6 units can be expressed as V = 6³ = 216. The area of a square with side lengths of 10 units can be expressed as A = 10² = 100. To find the product of the volumes of two cubes with side lengths of 7 units, you multiply the two exponential expressions, resulting in 117,649.

Step-by-step explanation:

To express the volume of a cube with side lengths of 6 units, you can use the integer expression V = s³, where V is the volume and s is the side length. So, the integer expression for the volume of the cube is V = 6³ = 216.

To express the area of a square with side lengths of 10 units, you can use the integer expression A = s², where A is the area and s is the side length. So, the integer expression for the area of the square is A = 10² = 100.

If you have two cubes, each with a side length of 7 units, you can write the exponential expressions as V₁ = 7³ = 343 and V₂ = 7³ = 343. To find the product of the two volumes, you simply multiply the two expressions: V₁ * V₂ = 343 * 343 = 117,649. Therefore, the integer expression for the product of the volumes of the two cubes is 117,649.