fill in the blanks

Question

according to the power of a power property, (7^(3/2))^2 =343 //blank fraction with exponent//, so there exists a number that has this square. Thus, 7^3/2=radical sign with two blanks

Answer 1

According to the power of a power property, \((7^{(3/2)})^2 = 7^{(3/2) \cdot 2} = 7^{3}\). Thus, there exists a number that has this square.

So, \(7^{3/2} = \sqrt[2]{7^3}\).

To fill in the blanks:

1. The blank fraction with exponent: 3
2. The expression for the radical sign with two blanks: √7³ or √(7^3).

So, it would be:

According to the power of a power property, \((7^{(3/2)})^2 = 7^{3}\), so there exists a number that has this square. Thus, \(7^{3/2} = \sqrt{7^3}\).