Question

(15^1/4 DIVIDED BY 3^1/2)^​-2

Answer 1

Dear student,

$$\begin{gathered} Tosolve:{\left(\frac{{15}^{{\displaystyle \frac{1}{4}}}}{3^{{\displaystyle \frac{1}{2}}}}\right)}^{-2} \\ ={\left(\frac{3^{\frac{1}{2}}}{{15}^{\frac{1}{4}}}\right)}^2......\left[{\left(\frac{a}{b}\right)}^{-1}=\left(\frac{b}{a}\right)\right] \\ =\frac{3^{\frac{1}{2}\times 2}}{{15}^{\frac{1}{4}\times 2}}......\left[{\left(a^m\right)}^n=a^{mn}\right] \\ =\frac{3}{{15}^{{\displaystyle \frac{1}{2}}}}=\frac{3}{\sqrt{3}\times \sqrt{5}}=\frac{3^{1-{\displaystyle \frac{1}{2}}}}{5^{{\displaystyle \frac{1}{2}}}}=\frac{3^{{\displaystyle \frac{1}{2}}}}{5^{\frac{1}{2}}}or\frac{\sqrt{3}}{\sqrt{5}} \end{gathered}$$

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