Question

Which of the following choices show a pair of equivalent expressions?

A. 6^2/7 and (sqrt6)^7
B. 7^5/7 and (sqrt7)^5
C. 5^(3/2) and (sqrt5)^3
D. (4sqrt81)^5 and 81^(5/4)

Answer 1

The pair of equivalent expressions is 6^2/7 and (sqrt6)^7.

Step-by-step explanation:

The pair of equivalent expressions is

1. A. 62/7 and (sqrt(6))7

To verify this, we need to simplify both expressions and check if they are equal.

1. For the first expression: 62/7 = 36/7, which is a rational number.
2. For the second expression: (sqrt(6))7 = (61/2)7 = 67/2 = (square root of 6)7, which is an irrational number.

Since the two expressions are not equal, the pair of equivalent expressions is

1. A. 62/7 and (sqrt(6))7