Question 214160
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I think you are trying to render:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt[\small{3}]{a}\,\cdot\,\sqrt[\small{5}]{a}]


The trick here is to recognize that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt[\small{n}]{x^m}\ =\ x^{\frac{m}{n}}]


So you have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^{\frac{1}{3}}\,\cdot\,a^{\frac{1}{5}}]


Next use:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^n\,\cdot\,x^m\ =\ x^{n+m}]


Then since:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{3} + \frac{1}{5} = \frac{8}{15}]


We have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a^{\frac{1}{3}}\,\cdot\,a^{\frac{1}{5}}\ =\ a^{\frac{8}{15}} = \sqrt[15]{a^8}]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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