You are painting a room that is 16 feet long, 10 feet wide, and 8 feet high. On the walls of the room, there are two windows that are each 2 feet wide and 5 feet tall, and a door that is 4 feet wide and 7 feet tall. A gallon of paint covers 350 square feet. How many gallons of paint do you need to cover the 4 walls with one coat of paint, not including the windows and the door

1.05 gallons

Step-by-step explanation:

Given that:

Dimension of wall : 16 by 10 by 8

Dimension of window : 2 by 5 feets

Number of windows = 2

Dimension of door = 4 by 7 feets

One gallon of paint = 350 ft²

Area of the four walls :

2 * height * (length + Width)

2 * 8 * (16 + 10)

2 * 8 * 26 = 416 ft²

Area of window :

2 * (2 * 5) = 20ft²

Area of door :

4 * 7 = 28 feet²

Area of wall without door and windows :

(416 - 20 - 28)ft² = 368 ft²

Gallon of paint required :

368 ft² / 350 ft²

= 1.05 gallons

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0