If $\left(\frac{2}{5}\right)^{5} \times\left(\frac{25}{4}\right)^{3}=\left(\frac{5}{2}\right)^{3 x-2},$ then find $x$.
Simplify
$3^{\frac{2}{3}} \cdot 3^{\frac{4}{3}}$
If $a=\frac{3+\sqrt{5}}{2},$ then find the value of $a^{2}+\frac{1}{a^{2}}$.
Rationalise the denominator in each of the following
$\frac{18}{3 \sqrt{2}-2 \sqrt{3}}$
For each question, select the proper option from four options given, to make the statement true : (Final answer only)
$\frac{\sqrt{50}}{\sqrt{98}}$ is a $\ldots \ldots \ldots$ number.