Question

A film set designer is using white and colored tiles in a pattern to create paths of different lengths. If x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule

(8x2y2)(3xy)

where y represents the number of white tiles.

Which simplified expression represents the number of colored tiles used for a path of length x feet?

24x3y3
11x3y3
24x2y2
11x2y2

Answer 1

Answer: 24x3y3

Explanation:

Answer 2

Option 1 -
`(8x^2y^2)(3xy)=24x^3y^3`

Explanation:

Given : A film set designer is using white and colored tiles in a pattern to create paths of different lengths. If x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule

`(8x^2y^2)(3xy)` where y represents the number of white tiles.

To find : Which simplified expression represents the number of colored tiles used for a path of length x feet?

Solution :

The number of colored tiles needed to make is
`(8x^2y^2)(3xy)`

Where, y represents the number of white tiles.

x represents the length of path in feet.

Simplifying the expression,

`(8x^2y^2)(3xy)`

`=8* 3* x^2* x* y^2* y`

We know,
`a^m* a^n=a^(m+n)`

`=24x^3y^3`

Therefore, Option 1 is correct.