Answer
$10x^{\frac{7}{12}}$
Work Step by Step
RECALL:
(i) $a^{-m} = \dfrac{1}{a^m}$
(ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$
(iii) $a^m \cdot a^n = a^{m+n}$
Use rule (ii) above to obtain:
$=5x^{\frac{1}{3}} \cdot 2x^{\frac{1}{4}}
\\=5(2)\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{4}}
\\=10\cdot x^{\frac{1}{3}}\cdot x^{\frac{1}{4}}
$
Use rule (iii) above to to obtain:
$=10\cdot x^{\frac{1}{3} + \frac{1}{4}}
\\=10x^{\frac{4}{12} + \frac{3}{12}}
\\=10x^{\frac{7}{12}}$
