Respuesta :
When you have fractions in the exponent, the denominator is the root and the numerator is the power on the number inside the root.
4^(1/7) = ⁷√(4)
4^(7/2) = √(4)^7
7^(1/4) = ⁴√(7)
7^(1/2) = √(7)
4^(1/7) = ⁷√(4)
4^(7/2) = √(4)^7
7^(1/4) = ⁴√(7)
7^(1/2) = √(7)
Answer:
Radical form refers to a form of an algebraic expression in which we have a number or an expression underneath a radical.
Any algebraic expression involving exponents then, we can write it in radical form based on the fact that [tex]x^{\frac{a}{n}}[/tex] is equivalent to the nth root of [tex]x^a[/tex] i.e,
[tex]x^{\frac{a}{n}}[/tex] =[tex]\sqrt[n]{x^a}[/tex]
Now, Consider the expression:
[tex]4^{\frac{1}{7}} = \sqrt[7]{4}[/tex]
[tex]4^{\frac{7}{2}} = \sqrt[2]{4^7}[/tex]
[tex]7^{\frac{1}{4}} = \sqrt[4]{7}[/tex]
[tex]7^{\frac{1}{2}} = \sqrt[2]{7}[/tex]