Mathematics, 10.11.2019 17:31 lakhanir2013
How can the properties of rational exponents be applied to simplify expressions with radicals or rational exponents?
Answers: 1
![\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \\\\\\ \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -----------------------------\\\\ \textit{let's say you have }\qquad \sqrt[27]{64^9} \\\\ \sqrt[27]{64^9}\implies 64^{\cfrac{}{}\frac{9}{27}}\quad \quad however\implies 64=4^3 \\\\ thus\qquad 64^{\cfrac{}{}\frac{9}{27}}\implies (4^3)^{\cfrac{}{}\frac{9}{27}}\implies (4)^{\cfrac{}{}3\cdot \frac{9}{27}}\implies 4^{\cfrac{}{}\frac{9}{9}}\implies 4^1\implies 4](/tpl/images/0368/1433/80650.png)
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