Question

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

Answer 1

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 2

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  $x^{\frac{a}{n}}$ is equivalent to the nth root of $x^a$ i.e,

$x^{\frac{a}{n}}$ =$\sqrt[n]{x^a}$

Now, Consider the expression:

$4^{\frac{1}{7}} = \sqrt[7]{4}$

$4^{\frac{7}{2}} = \sqrt[2]{4^7}$

$7^{\frac{1}{4}} = \sqrt[4]{7}$

$7^{\frac{1}{2}} = \sqrt[2]{7}$