Question

Which is equivalent to7^(3/2) over 7^(1/2)?

A. 7^(1/3)
B. 7^(3/4)
C. 7^1
D. 7^2
E. 7^3

Answer 1

the answer is c! you just subtract: 3/2-1/2, which is 1.

Answer 2

Given the expression below:

`\large{ \frac{ {7}^{ (3)/(2) } }{ {7}^{ (1)/(2) } } }`

Use the following property:

`\large \boxed{ {a}^{ (m)/(n) } = \sqrt[n]{ {a}^(m) } }`

Therefore:

`\large{ \frac{ {7}^{ (3)/(2) } }{ {7}^{ (1)/(2) } } = \frac{ \sqrt{ {7}^(3) } }{ √(7) } } \\ \large{ \frac{ \sqrt{ {7}^(3) } }{ √(7) } = ( √(7 * 7 * 7) )/( √(7) ) \longrightarrow (7 √(7) )/( √(7) ) } \\ \large{ \frac{7 \cancel{ √(7) }}{ \cancel{ √(7) }} = 7}`

Note that a¹ = a. Therefore, 7¹ = 7.

Answer

• 7¹ or 7.