Simplify the following expression.
[(1 + p)(1 + p²)(1 + p⁴)(1 + p⁸)(1 + p¹⁶)(1 - p) - 1]

Given that $$x = 4\sqrt{12} + 5\sqrt{27 }– 3\sqrt{75 }+ \sqrt{300}$$​ and y = $$(2 + \sqrt3)(2 – \sqrt3).$$​ If $$\frac x y = a + b\sqrt3,$$​ then what is the value of (a + 2b)?

If  $$\frac{4\sqrt{6} - 6\sqrt{2}}{\sqrt{96} + \sqrt{72}} \times \frac{1}{7 + \sqrt{48}} = a + b\sqrt{3}$$​, then what is the value of (a + b) ?

Find the value of $$55^{-6} \div 55^{5} \times 55^{-8}$$.​

If $$\frac{\sqrt{121}\times \sqrt{52-14\sqrt{3}}}{\sqrt{28+10\sqrt{3}}}=a+b\sqrt{3},$$​​
then find the value of (a+b).

If x$$=\frac{\sqrt{1875}}{\sqrt{3888}} \div \frac{\sqrt{1200}}{\sqrt{768}} \times \frac{\sqrt{175}}{\sqrt{1792}}$$. Find $$\sqrt x$$.​

If $$m=\frac{2^{5}\times (3^{5})^{2}}{12\times 81\times 3^{3}},$$​ $$n=\frac{(2^{-4})^{2}\times 2^{-5}}{4^{-3}}$$​then what is the value of $$\sqrt{mn}$$​ ?

Which of the following is correct?
(i) √7 + √2 > √6 + √3
(ii) √7 + √2 < √6 + √3
(iii) √7 + √2 = √6 + √3

Find the value of $$\left(\frac{1}{4}\right)^{-2} + \left(\frac{1}{9}\right)^{-2} + \left(\frac{1}{7}\right)^{-2}$$​​

Find the value of: 26⁻¹⁹ ÷ 26¹⁸ × 26³

The value of $$10^2 + \sqrt{2^2} - 4\sqrt{25} - 3$$​ is