Question

How can the properties of rational exponent be applied to simplify expressions with radicals or rational exponents?

Answer 1

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\qquad thus\\ ----------------------------\\\\ say\implies \sqrt[6]{216}\implies \sqrt[6]{6^3}\implies 6^{\frac{3}{6}}\implies 6\frac{1}{2}\implies \sqrt{6}$

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