કિંમત શોધો: $\frac{\sqrt{2}}{\sqrt{2 + \sqrt{3}} - \sqrt{2 - \sqrt{3}}}$

$({x^5})^{1/3} \times (16{x^3})^{2/3} \times \left( \frac{1}{4}{x^{4/9}} \right)^{-3/2} = ?$

જો ${\left( \frac{2}{3} \right)^{x + 2}} = {\left( \frac{3}{2} \right)^{2 - 2x}}$ હોય,તો $x =$

$x \ne 0$ માટે,${\left( {\frac{{{x^l}}}{{{x^m}}}} \right)^{({l^2} + lm + {m^2})}} {\left( {\frac{{{x^m}}}{{{x^n}}}} \right)^{({m^2} + nm + {n^2})}} {\left( {\frac{{{x^n}}}{{{x^l}}}} \right)^{({n^2} + nl + {l^2})}}$ ની કિંમત શોધો.

જો $\frac{{({2^{n + 1}})^m}({2^{2n}}){2^n}}{{({2^{m + 1}})^n}{2^{2m}}} = 1$ હોય,તો $m =$

પદાવલિનું મૂલ્ય શોધો: $\frac{2 \cdot 3^{n+1} + 7 \cdot 3^{n-1}}{3^{n+2} - 2 \cdot (1/3)^{1-n}}$