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6. (2⁻¹ a³ b⁻⁴/4 a⁻² b)⁻¹
= [(1/(2 . 4) a⁽³⁻⁽⁻²⁾⁾ b⁽⁻⁴⁻¹⁾]⁻¹
= (1/8 a⁵ b⁻⁵)⁻¹
= 8 a⁻⁵ b⁵
8. (9 . 3⁻³ + 2 . 3⁻¹)/2
= (9 . 1/27 + 2 . 1/3)/2
= (9/27 + 2/3)/2
= (9/27 + 18/27)/2
= (27/27)/2
= 1/2
9. (1/16)⁻¹/⁴ + 27²/³ - 9³/²
= 16¹/⁴ + 27²/³ - 9³/²
= (2⁴)¹/⁴ + (3³)²/³ - (3²)³/²
= 2¹ + 3² - 3³
= 2 + 9 - 27
= -16
10. 5√20 + 3√135 - √45
= 5√(2² . 5) + 3√(3² . 15) - √(3² . 5)
= 5 . 2√5 + 3 . 3√15 - 3√5
= 10√5 + 9√15 - 3√5
= 7√5 + 9√15