All 100 targets have a solution.
\(1 = 68^{9 - 9 }\)
\(2 = 98 - 96 \)
\(3 = 8 \cdot 9 - 69 \)
\(4 = \frac{ \frac{ 96 }{ 8 } }{ \sqrt{9 } }\)
\(5 = 86 - 9 \cdot 9 \)
\(6 = ( 8 \cdot 9 - 69 )!\)
\(7 = 96 - 89 \)
\(8 = 9 - ( 9 - 8 )^{6 }\)
\(9 = \frac{ 69 + \sqrt{9} }{ 8 }\)
\(10 = ( 9 - 8 )^{6} + 9 \)
\(11 = \frac{ 9 }{ 9 - 6 } + 8 \)
\(12 = \sqrt{\sqrt{9}^{8}} - 69 \)
\(13 = 99 - 86 \)
\(14 = 6 + 8 - 9 + 9 \)
\(15 = \frac{ 69 }{ \sqrt{9} } - 8 \)
\(16 = 9 - ( 8 - 6 ) + 9 \)
\(17 = ( 8 - 6 )^{\sqrt{9}} + 9 \)
\(18 = 98 - \frac{ 6! }{ 9 }\)
\(19 = ( 9 - 6 ) \cdot 9 - 8 \)
\(20 = 89 - 69 \)
\(21 = \frac{ 96 }{ 8 } + 9 \)
\(22 = \sqrt{9}!! - 698 \)
\(23 = ( 9 - 6 )! + 8 + 9 \)
\(24 = 96 - 8 \cdot 9 \)
\(25 = \frac{ 6 \cdot 8 }{ \sqrt{9} } + 9 \)
\(26 = 6 + 8 + \sqrt{9} + 9 \)
\(27 = ( 8 - 6 ) \cdot 9 + 9 \)
\(28 = ( 9 - \sqrt{9} ) \cdot 6 - 8 \)
\(29 = 98 - 69 \)
\(30 = 6 \cdot 8 - 9 - 9 \)
\(31 = 99 - 68 \)
\(32 = 6 + 8 + 9 + 9 \)
\(33 = ( 9 - 6 ) \cdot 8 + 9 \)
\(34 = \frac{ ( 8 + 9 ) \cdot 6 }{ \sqrt{9 } }\)
\(35 = 89 - 6 \cdot 9 \)
\(36 = \frac{ 96 }{ 8 } \cdot \sqrt{9 }\)
\(37 = 6 \cdot 9 - 8 - 9 \)
\(38 = \frac{ 8! }{ 6! } - 9 - 9 \)
\(39 = \sqrt{89 \cdot 9 + 6 !}\)
\(40 = \frac{ 96 }{ \sqrt{9} } + 8 \)
\(41 = 68 - \sqrt{9} \cdot 9 \)
\(42 = ( 8 - \frac{ 9 }{ 9 } ) \cdot 6 \)
\(43 = 99 - \frac{ 8! }{ 6 ! }\)
\(44 = 98 - 6 \cdot 9 \)
\(45 = 69 - 8 \cdot \sqrt{9 }\)
\(46 = ( 9 - 6 )! \cdot 9 - 8 \)
\(47 = 6 \cdot 8 - \frac{ 9 }{ 9 }\)
\(48 = 6 \cdot 8 - 9 + 9 \)
\(49 = \frac{ 98 \cdot \sqrt{9} }{ 6 }\)
\(50 = 68 - 9 - 9 \)
\(51 = 99 - 6 \cdot 8 \)
\(52 = 69 - 8 - 9 \)
\(53 = 6 \cdot 9 + 8 - 9 \)
\(54 = ( 9 - 8 ) \cdot 6 \cdot 9 \)
\(55 = 6 \cdot 9 - 8 + 9 \)
\(56 = 68 - 9 - \sqrt{9 }\)
\(57 = 8 \cdot 9 - 6 - 9 \)
\(58 = 69 - 8 - \sqrt{9 }\)
\(59 = 68 - \sqrt{9 \cdot 9 }\)
\(60 = ( 9 - 8 + 9 ) \cdot 6 \)
\(61 = 8^{\frac{ 6 }{ \sqrt{9} }} - \sqrt{9 }\)
\(62 = 68 - 9 + \sqrt{9 }\)
\(63 = ( 9 - ( 8 - 6 ) ) \cdot 9 \)
\(64 = 69 - 8 + \sqrt{9 }\)
\(65 = 68 - \frac{ 9 }{ \sqrt{9 } }\)
\(66 = 6 \cdot 8 + 9 + 9 \)
\(67 = 68 - \frac{ 9 }{ 9 }\)
\(68 = 68 - 9 + 9 \)
\(69 = \frac{ 9 }{ 9 } + 68 \)
\(70 = 69 - 8 + 9 \)
\(71 = \frac{ 9 }{ \sqrt{9} } + 68 \)
\(72 = 96 - 8 \cdot \sqrt{9 }\)
\(73 = 8^{\frac{ 6 }{ \sqrt{9} }} + 9 \)
\(74 = 89 - 6 - 9 \)
\(75 = 8 \cdot 9 - 6 + 9 \)
\(76 = \frac{ \frac{ 9! }{ 6! } }{ \sqrt{9}! } - 8 \)
\(77 = \sqrt{9 \cdot 9} + 68 \)
\(78 = \frac{ 9! }{ 8! } + 69 \)
\(79 = 96 - 8 - 9 \)
\(80 = 68 + \sqrt{9} + 9 \)
\(81 = 89 \cdot 9 - 6 !\)
\(82 = 96 - 8 - \sqrt{9 }!\)
\(83 = 98 - 6 - 9 \)
\(84 = 9^{8 - 6} + \sqrt{9 }\)
\(85 = 86 - \frac{ 9 }{ 9 }\)
\(86 = 68 + 9 + 9 \)
\(87 = \frac{ 9 }{ 9 } + 86 \)
\(88 = 89 - \frac{ 6 }{ \sqrt{9 }! }\)
\(89 = \frac{ 9 }{ \sqrt{9} } + 86 \)
\(90 = 9^{8 - 6} + 9 \)
\(91 = \frac{ 6 }{ \sqrt{9} } + 89 \)
\(92 = 89 - 6 + 9 \)
\(93 = 8 \cdot \sqrt{9} + 69 \)
\(94 = 96 - 8 + \sqrt{9 }!\)
\(95 = 96 + 8 - 9 \)
\(96 = ( 9 - 8 ) \cdot 96 \)
\(97 = 96 - 8 + 9 \)
\(98 = 86 + \sqrt{9} + 9 \)
\(99 = \sqrt{99^{8 - 6 }}\)
\(100 = \frac{ 6 }{ \sqrt{9} } + 98 \)