What is the radical form of each of the given expressions?

Drag the answer into the box to match each expression.

4 1/7------------_____
4 7/2-----------_____
7 1/4------------_____
7 1/2------------_____

please fill in the _ here are the options

sqrt (7^2) , sqrt (4^7) , ^7 sqrt (4) , ^4 sqrt (7) , sqrt (7)

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)

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]