Question

$9 \frac{1}{2} \times27 \frac{1}{2 } \\ \\ 3 \frac{ - 1}{2} \times 3 \frac{1}{3}$

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Answer 1

Simplify:

Step-by-step explanation:

$\ Given \ value:\\\\\frac{9^{\frac{1}{2}}\times 27^{\frac{1}{2}}}{3^{-\frac{1}{6}}\times 3^{\frac{1}{3}}}\\\\\ Solution:\\\\\frac{9^{\frac{1}{2}}\times 27^{\frac{1}{2}}}{3^{-\frac{1}{6}}\times 3^{\frac{1}{3}}}\\\\\ apply \ formula:\\\\((a^b)^c ) = a^{(b\times c)} \\\\a^b \times a^c = a^{(b+c)}\\\\\frac{a^b}{a^c} = a^{(b-c)}\\\\\rightarrow \frac{(3^2)^{\frac{1}{2}}\times 27^{\frac{1}{2}}}{3^{-\frac{1}{6}}\times 3^{\frac{1}{3}}}\\\\\rightarrow 3^{1 + \frac{3}{2} + \frac{1}{6} - \frac{1}{3}}$

$\rightarrow 3^{\frac{6+9+1-2}{6}}\\\\\rightarrow 3^{\frac{14}{6}}\\\\\rightarrow 3^{\frac{7}{3}}$

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