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If \(5^{(x + 2y)} = 5\) and \(4^{(x + 3y)} = 16\), find \(3^{(x + y)}\).
Simplify \(\frac{1}{5x + 5}\) + \(\frac{1}{7x+ 7}\)
Solve the equation 3x\(^2\) + 6x - 2 = 0
Factorize \(x^2 + 2a + ax + 2x\)
Find all real numbers x which satisfy the inequality \(\frac{1}{3}\)(x + 1) - 1 > \(\frac{1}{5}\)(x + 4)
If y = \(\frac{x}{x - 3}\) + \(\frac{x}{x + 4}\) find y when x = -2
Factorize completely 8a + 125ax\(^3\)
Simplify \(\frac{9^{\frac{1}{3}} \times 27^{-\frac{1}{2}}}{3^{-\frac{1}{6}} \times 3^{\frac{-2}{3}}}\)
Find n if log\(_{2}\) 4 + log\(_{2}\) 7 - log\(_{2}\) n = 1
Simplify \((\frac{1}{\sqrt{5} + \sqrt{3}} - \frac{1}{\sqrt{5} - \sqrt{3}}) \times \frac{1}{\sqrt{3}}\)
If P = 18, Q = 21, R = -6 and S = -4, Calculate \(\frac{(P- Q)^3 + S^2}{R^3}\)
Find the reciprocal of \(\frac{\frac{2}{3}}{\frac{1}{2} + \frac{1}{3}}\)