Higher roots formulas formulas

a, b

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Positive real numbers

m, n

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Integers

Root of a product

$\sqrt[n]{ab}=\sqrt[n]{a} \cdot \sqrt[n]{b}$

Root of a fraction

$\sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}$

Product of roots

$\sqrt[n]{a} \cdot \sqrt[m]{b} = \sqrt[mn]{a^mb^n}$

Quotione of roots

$\dfrac{\sqrt[n]{a}}{\sqrt[m]{b}}=\sqrt[nm]{\dfrac{a^m}{b^n}}$

Power of a root

$\left(\sqrt[n]{a^m}\right)^p=\sqrt[n]{a^{mp}}$

$\left(\sqrt[n]{a}\right)^n=a$

$\sqrt[n]{a^m}=\sqrt[np]{a^{mp}}$

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

Root of a root

$\sqrt[m]{\sqrt[n]{a}}=\sqrt[mn]{a}$

10.

Power of a root

$\left(\sqrt[n]{a}\right)^m=\sqrt[n]{a^m}$

11.

Rationalize fractions

$\dfrac{1}{\sqrt[n]{a}}= \dfrac{\sqrt[n]{a^{n-1}}}{a}$