Evaluate: \(\frac { \sqrt [ 3 ]{ 2 } .{ 4 }^{ 3/2 } }{ { 128 }^{ 1/3 } } \)

If x = 5 and y = 2, find the value of \((i)\quad \left( { x }^{ y }+{ y }^{ y } \right) \ (ii)\ { \left( { x }^{ y }+{ y }^{ y } \right) }^{ -1 }\)

If \(\frac { 2+\sqrt { 3 } }{ 2-\sqrt { 3 } } +\frac { 2-\sqrt { 3 } }{ 2+\sqrt { 3 } } +\frac { \sqrt { 3 } -1 }{ \sqrt { 3 } +1 } =a+b\sqrt { 3 } \quad \) , find the rational numbers a and b.

Classify the following numbers as rational or irrational: \(2\pi \)

If \(a=\frac { \sqrt { 3 } +1 }{ \sqrt { 3 } -1 } \) and \(b=\frac { 1 }{ a } \) , find the value of \({ a }^{ 2 }+ab+{ b }^{ 2 }\)

If \(a=\frac { \sqrt { 2 } +1 }{ \sqrt { 2 } -1 } \) and \(b=\frac { 1 }{ a } \), find the value of \({ a }^{ 2 }+{ b }^{ 2 }\)

If \(x=3+2\sqrt { 2 } \) , find the value of \({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \)

Rationalize the denominator of \(\frac { 1 }{ \sqrt { 2 } } \)

Simplify: (5²)^-7

Simplify: 17².17⁵

Represent \(0.\overline { 237 } \) in the form p/q, where p and q are integers and \(q\neq 0\)

Express \(0.\overline { 001 } \) as a rational number in the form p/q, where p and q are integers and \(q\neq 0\)

Find two rational numbers between 0.1 and 0.2.