What is a rational exponent and how does it relate to radical expressions?

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

Which is an equivalent expression for \( \left(3^{2} \cdot 5^{4}\right)^{3} ? \) \( 3^{2} \cdot 5^{12} \) \( 3^{5} \cdot 5^{7} \) \( 3^{6} \cdot 5^{12} \) \( 15^{18} \)

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

Use the recursively defined geometric sequence \( a_{1}=\frac{5}{6}, a_{n}=4 a_{n-1} \) and find the common ratio. (1 point) \( 0 \frac{5}{6} \) \( 0-\frac{2}{3} \) \( 0 \frac{10}{3} \)

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