Calculus with Applications (10th Edition)

$\sqrt[6]{a^5}$
RECALL: (i) $a^m \cdot a^n = a^{m+n}$ (ii) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (iii) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$ Use rule (ii) to have: $=a^{\frac{1}{2}}\cdot a^{\frac{1}{3}}$ Use rule (i) to have: $\\=a^{\frac{1}{2} + \frac{1}{3}} \\=a^{\frac{3}{6} + \frac{2}{6}} \\=a^{\frac{5}{6}}$ Use rule (iii) to have: $=\sqrt[6]{a^5}$
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