- (a) Given that \(8 = 2 ^ { k }\), write down the value of \(k\).
(b) Given that \(4 ^ { x } = 8 ^ { 2 - x }\), find the value of \(x\). - Given that \(( 2 + \sqrt { } 7 ) ( 4 - \sqrt { 7 } ) = a + b \sqrt { } 7\), where a and \(b\) are integers,
(a) find the value of a and the value of \(b\).
Given that \(\frac { 2 + \sqrt { 7 } } { 4 + \sqrt { 7 } } = c + d \sqrt { 7 }\) where \(c\) and \(d\) are rational numbers,
(b) find the value of \(c\) and the value of \(d\).