Question

the floor of the commons room at king middle school is in the shape of a square with the side lengths of x^2 y^3. new tile is going to be put in the floor if the room. find the area of the floor

Answer 1

We are given: The length of the square floor of common room = x^2y^3.

We need to find the area of the floor to room to be covered with the new tiles.

Solution: The shape of the floor is a square.

We know the formula of the square is given by

Area of a square = Side * side = (side )^2

Plugging value of side length x^2y^3 in formula of area, we get

Area of a square floor =
`(x^2y^3)^2`.

In order to simplify, we need to apply Power of Power rule of exponents.

According to Power of Power rule of exponents the whole power is to be distribute over the exponents inside parenthesis.

Therefore,

`(x^2y^3)^2`=
`x^(2*2) y{3*2}` =
`x^4y^6`

So, the expression for area of the floor is
`x^4y^6` feet square.

Answer 2

The shape of the common room's floor is square

Side length of the square = x²y³

Area of the square = Side²

⇒ Area of the square = (x²y³)²

⇒ Area of the square = x⁴y⁶

Hence the area of the room is x⁴y⁶ square units.