Answer: the actual length and width of the room is 24ft by 36ft
Step-by-step explanation:
The scale on the architectural plans for a new house is 1 in. equals 4 ft. This means that every 1 inch on the on the architectural plan represents 4 feet on the actual building.
Therefore, if the length of the room as measured on the drawing is 6 inches, the actual length of the room will be
6 × 4 = 24 feet
Also, if the width of the room as measured on the drawing is 9 inches, the actual width of the room will be
9 × 4 = 36 feet
You just need to equate the expressions to find the values for a,b and c. First, let's settle that 2^5/4=8, and 8 is 2^3. Also, an important tool here is the indicie rule:

1st expression: 2^5/4=8
2nd expression: It tells us that 2^5/2^a=2^3 (I know that this equals to 8 as all the expressions are equal therefore is the same as our first expression). Using the indicie law, this means that a=2
3rd expression: 2^b must equal to 8 as well, so b=3
4th expression: c=8 as all of the other expressions we have figured out equal to 8
So a=2, b=3 and c=8
You could multiply 6 times 3 to get your answer. The answer would be 18