What is the radical form of each of the given expressions?
2 answers:
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
is equivalent to the nth root of
i.e,
=![\sqrt[n]{x^a}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%5Ea%7D)
Now, Consider the expression:
![4^{\frac{1}{7}} = \sqrt[7]{4}](https://tex.z-dn.net/?f=4%5E%7B%5Cfrac%7B1%7D%7B7%7D%7D%20%3D%20%5Csqrt%5B7%5D%7B4%7D)
![4^{\frac{7}{2}} = \sqrt[2]{4^7}](https://tex.z-dn.net/?f=4%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D%20%3D%20%5Csqrt%5B2%5D%7B4%5E7%7D)
![7^{\frac{1}{4}} = \sqrt[4]{7}](https://tex.z-dn.net/?f=7%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%20%3D%20%5Csqrt%5B4%5D%7B7%7D)
![7^{\frac{1}{2}} = \sqrt[2]{7}](https://tex.z-dn.net/?f=7%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%3D%20%5Csqrt%5B2%5D%7B7%7D)
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