Simplify \(\left( 125 \right) ^{ \frac { 2 }{ 3 } }\)

Evaluate \(\left( \left[ (256)^{ \frac { -1 }{ 2 } } \right] ^{ \frac { -1 }{ 4 } } \right) ^{ 3 }\)

Simplify and hence find the value of n: \(3^{2 n} 9^{2} 3^{-n} / 3^{3 n}=27\)

Find the radius of the spherical tank whose volume is  \(\frac { 32\pi }{ 3 } \) units

Solve for x  \(\left| 3-x \right| <7\)

Represent the following inequalities in the interval notation:
\(x\le 5\) and \(x\ge -3\)

Represent the following inequalities in the interval notation:
\(x<-1\) or \(x<3\)

Let b > 0 and b ≠ 1. Express y = b^x in logarithmic form. Also state the domain and range of the logarithmic function.

A quadratic polynomial has one of its zeros as \(1+\sqrt { 5 } \) and it satisfies p(1) = 2. Find the quadratic polynomial.

Discuss the nature of roots of 9x² + 5x = 0.