Question

solve it quickly by step by step explanation ​

Answer 1

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To Simplify:

• $\dfrac{9^{\frac{1}{3}} \times 27^{\frac{-1}{2}}}{3^{\frac{1}{6}} \times 3^{\frac{-2}{3}}}$

Solution:

$\implies \dfrac{9^{\frac{1}{3}} \times 27^{\frac{-1}{2}}}{3^{\frac{1}{6}} \times 3^{\frac{-2}{3}}} \\ \\ \implies \dfrac{9^{\frac{1}{3}} \times 3^{\frac{2}{3}}}{3^{\frac{1}{6}} \times 27^{\frac{1}{2}}} \\ \\ \implies \dfrac{3^{\frac{2}{3}} \times 3^{\frac{2}{3}}}{3^{\frac{1}{6}} \times 3^{\frac{3}{2}}} \\ \\ \implies 3^{\frac{2}{3} + \frac{2}{3} - \frac{1}{6} - \frac{3}{2}} \\ \\ \implies 3^{\frac{4 + 4 - 1 - 9}{6}} \\ \\ \implies 3^{\frac{-2\!\!\!\!/^{-1}}{6\!\!\!\!/_{\:\:3}}} \\ \\ \implies 3^{\frac{-1}{3}} \\ \\ \bold{ \implies \dfrac{1}{3}^{\frac{1}{3}} }$

Formula Used:

• $a^m \times a^n = a^{m+n}$
• $\dfrac{a^m}{a^n} = a^{m-n}$
• $a^{-m} = \dfrac{1}{a}^m$

Learn More:

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$