Simplify : 2 a^ 1 2 a^ 2 3 6 a^ -7 3 9 a^ -5 3 a^ 3 2 , if a=4. - Vidyadip

Question

Simplify : $\frac{2 a^{\frac{1}{2}} \times a^{\frac{2}{3}} \times 6 a^{\frac{-7}{3}}}{9 a^{\frac{-5}{3}} \times a^{\frac{3}{2}}}$, if $a=4$.

✓

Answer

$\frac{2 a^{\frac{1}{2}} \cdot a^{\frac{2}{3}} \times 6 a^{\frac{-7}{3}}}{9 a^{\frac{-5}{3}} \times a^{\frac{3}{2}}}=\frac{2.2 .3 \cdot a^{\frac{1}{2}+\frac{2}{3}-\frac{7}{3}}}{3.3 a^{\frac{-5}{3}+\frac{3}{2}}}$
$=\frac{4}{3} \frac{a^{\frac{3+4-14}{6}}}{a^{\frac{-10+9}{6}}}$
$=\frac{4}{3} \frac{a^{\frac{-7}{6}}}{a^{\frac{-1}{6}}}$
$=\frac{4}{3} a^{\frac{-7}{6}+\frac{1}{6}}$
$\begin{array}{l}=\frac{4}{3} a^{\frac{-6}{6}} \\ =\frac{4}{3} a^{-1}\end{array}$
$=\frac{4}{3} \cdot \frac{1}{a}$
$=\frac{4}{3} \cdot \frac{1}{4}$[Given $a=4$ ]
$=\frac{1}{3}$.

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