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fill in the blanks
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
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
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GPT-4o mini
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, \(7^{3/2} = \sqrt{7^3}\).
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, \(7^{3/2} = \sqrt{7^3}\).