QS Express each of the following having a ralional denominator: \[ \frac{1}{1+\sqrt{2}+\sqrt{3}} \]

Choose an equivalent expression for \( \left(\left(\frac{2}{5}\right)^{4}\left(\frac{2}{5}\right)^{3}\right)^{2} \)

8. \( \left(4^{\frac{1}{5}}\right)\left(4^{\frac{3}{10}}\right) \)

\( \frac { 1 } { r } \times \frac { 1 - ( \frac { 1 } { r } ) ^ { n } } { 1 - \frac { 1 } { r } } \geq \frac { 9 r } { 100 } \Rightarrow 1 - \frac { 1 } { r ^ { n } } \geq \frac { 9 r } { 100 } \)

(c) Subtract: \( 31(1-4 m+5 n) \) from \( 4 I(10 n-3 m+21) \) (d) Subtract: \( 3 a(a+b+c)-2 b(a-b+c) \) from \( 4 c(-a+b+c \)

Given that the quadratic equation \( p x^{2}-9 q x+9 p=0 \), where \( p \) and \( q \) are constants, has two equal roots. Find \( p: q \). [2 marks.