Question

(3/4) to the power of 5 (3/4) simplified

Answer 1

Answer:

729/4096

Step-by-step explanation:

Simplify the following:

(3/4)^5 3/4

(3/4)^5 3/4 = ((3/4)^5 3)/4:

((3/4)^5 3)/4

(3/4)^5 = 3^5/4^5:

(3^5/4^5 3)/4

3^5 = 3×3^4 = 3 (3^2)^2:

((3 (3^2)^2)/4^5 3)/4

4^5 = 4×4^4 = 4 (4^2)^2:

((3 (3^2)^2)/(4 (4^2)^2) 3)/4

4^2 = 16:

((3 (3^2)^2)/(4×16^2) 3)/4

3^2 = 9:

((3×9^2)/(4×16^2) 3)/4

| 1 | 6

× | 1 | 6

| 9 | 6

1 | 6 | 0

2 | 5 | 6:

((3×9^2)/(4×256) 3)/4

9^2 = 81:

((3×81)/(4×256) 3)/4

4×256 = 1024:

((3×81)/1024×3)/4

3×81 = 243:

(243/1024×3)/4

243/1024×3 = (243×3)/1024:

((243×3)/1024)/4

((243×3)/1024)/4 = (243×3)/(1024×4):

(243×3)/(1024×4)

1024×4 = 4096:

(243×3)/4096

243×3 = 729:

Answer: 729/4096