Question

Select all that are equal to 5^3*5^-7

a. 1/5^-4
b. 1/5^4
c. 5^-4
d. 5^4
e. 1/-625

Answer 1

5^3*5^-7 = 1/5^4 b. is true = 625

5^3*5^-7 = 5^-4 c. is true = 625

Explanation:

b. Left hand side

Simplify the following:

5^3/5^7

Combine powers. 5^3/5^7 = 5^(3 - 7):

5^(3 - 7)

3 - 7 = -4:

5^(-4)

5^4 = (5^2)^2:

1/(5^2)^2

5^2 = 25:

1/25^2

| 2 | 5

× | 2 | 5

1 | 2 | 5

5 | 0 | 0

6 | 2 | 5:

Answer: 1/625

Right hand side:

Simplify the following:

1/5^4

5^4 = (5^2)^2:

1/(5^2)^2

5^2 = 25:

1/25^2

| 2 | 5

× | 2 | 5

1 | 2 | 5

5 | 0 | 0

6 | 2 | 5:

Answer: 1/625

_____________________________

c. Left hand side (see above)

Right hand side:

Simplify the following:

5^(-4)

5^4 = (5^2)^2:

1/(5^2)^2

5^2 = 25:

1/25^2

| 2 | 5

× | 2 | 5

1 | 2 | 5

5 | 0 | 0

6 | 2 | 5:

Answer: 1/625

Answer 2

The answers are B and C. The other person is wrong.

Explanation: