Question

Which choice represents the fraction below as a single exponential expression?

8^4/8^16

a. 8^12
b. 8^4
c. 1/4
d. 8^-12

Answer 1

8^-12

Explanation:

Simplify the following:

8^4/8^16

Combine powers. 8^4/8^16 = 8^(4 - 16):

8^(4 - 16)

4 - 16 = -(16 - 4):

8^(-(16 - 4))

| 1 | 6

- | | 4

| 1 | 2:

8^(-12)

8^12 = (8^6)^2 = ((8^3)^2)^2 = ((8×8^2)^2)^2:

1/((8×8^2)^2)^2

8^2 = 64:

1/((8×64)^2)^2

8×64 = 512:

1/(512^2)^2

| | | 5 | 1 | 2

× | | | 5 | 1 | 2

| | 1 | 0 | 2 | 4

| | 5 | 1 | 2 | 0

2 | 5 | 6 | 0 | 0 | 0

2 | 6 | 2 | 1 | 4 | 4:

1/262144^2

| | | | | 2 | 6 | 2 | 1 | 4 | 4

× | | | | | 2 | 6 | 2 | 1 | 4 | 4

| | | | 1 | 0 | 4 | 8 | 5 | 7 | 6

| | | 1 | 0 | 4 | 8 | 5 | 7 | 6 | 0

| | | 2 | 6 | 2 | 1 | 4 | 4 | 0 | 0

| | 5 | 2 | 4 | 2 | 8 | 8 | 0 | 0 | 0

1 | 5 | 7 | 2 | 8 | 6 | 4 | 0 | 0 | 0 | 0

5 | 2 | 4 | 2 | 8 | 8 | 0 | 0 | 0 | 0 | 0

6 | 8 | 7 | 1 | 9 | 4 | 7 | 6 | 7 | 3 | 6:

Answer: 1/68719476736 = 8^-12