## Intermediate Algebra for College Students (7th Edition)

$\sqrt[10]{x^9}$
RECALL: (i) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ (iii) $(ab)^m = a^mb^m$ (iv) $(a^m)^n=a^{mn}$ (v) $a^m \cdot a^n = a^{m+n}$ Use rules (i) and (ii) above to obtain: $=x^{\frac{2}{5}} \cdot x^{\frac{1}{2}}$ Use rule (v) above to obtain: $=x^{\frac{2}{5}+\frac{1}{2}} \\=x^{\frac{4}{10} + \frac{5}{10}} \\=x^{\frac{9}{10}}$ Use rule (ii) to obtain: $\\=\sqrt[10]{x^9}$