Question

please solve the solution tommorow is my exam

Answer 1

$\frac{ {( - 3)}^{24} \times {( - 3)}^{17} \times {(8)}^{ - 9} }{ {(12)}^{16} \times {(27)}^{6} } \\ \\ = \frac{ {( - 3)}^{24} \times {( - 3)}^{17} \times {( {2}^{3} )}^{ - 9} }{ {( {2}^{2} \times 3 )}^{16} \times {( {3}^{3} )}^{6} } \\ \\ = \frac{ {( - 3)}^{24} \times {( - 3)}^{17} \times {(2)}^{ - 9 \times 3} }{ { {(2)}^{2 \times 16} \times (3) }^{16} \times {( 3 )}^{3 \times 6} } \\ \\ = \frac{ {( - 3)}^{24 + 17} \times {( 2)}^{ - 27} }{ {{(2)}^{32} \times( 3 )}^{16} \times {( 3)}^{18} }$

$= \frac{ {( - 3)}^{41} \times {( 2)}^{ - 27} }{ {{(2)}^{32} \times( 3 )}^{16 + 18}} \\ \\ = \frac{ - 1 \times {(3)}^{41} \times {( 2)}^{ - 27} }{ {{(2)}^{32} \times( 3 )}^{34}} \\ \\ = - 1 \times \frac{ {3}^{41} }{ {3}^{34} } \times \frac{ {2}^{ - 27} }{ {2}^{32} } \\ \\ = - 1 \times {3}^{(41 - 34)} \times {2}^{ (- 27 - 32)} \\ \\ = - 1 \times {3}^{7} \times {2}^{ - 59} \\ \\ = - \frac{ {3}^{7} }{ {2}^{59} }$

Answer 2

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$\frac{ {( - 3)}^{24} \times {( - 3)}^{17} \times {(8)}^{ - 9} }{ {(12)}^{16} \times {(27)}^{6} } \\ \\ = \frac{ {( - 3)}^{24} \times {( - 3)}^{17} \times {( {2}^{3} )}^{ - 9} }{ {( {2}^{2} \times 3 )}^{16} \times {( {3}^{3} )}^{6} } \\ \\ = \frac{ {( - 3)}^{24} \times {( - 3)}^{17} \times {(2)}^{ - 9 \times 3} }{ { {(2)}^{2 \times 16} \times (3) }^{16} \times {( 3 )}^{3 \times 6} } \\ \\ = \frac{ {( - 3)}^{24 + 17} \times {( 2)}^{ - 27} }{ {{(2)}^{32} \times( 3 )}^{16} \times {( 3)}^{18} }$

$= \frac{ {( - 3)}^{41} \times {( 2)}^{ - 27} }{ {{(2)}^{32} \times( 3 )}^{16 + 18}} \\ \\ = \frac{ - 1 \times {(3)}^{41} \times {( 2)}^{ - 27} }{ {{(2)}^{32} \times( 3 )}^{34}} \\ \\ = - 1 \times \frac{ {3}^{41} }{ {3}^{34} } \times \frac{ {2}^{ - 27} }{ {2}^{32} } \\ \\ = - 1 \times {3}^{(41 - 34)} \times {2}^{ (- 27 - 32)} \\ \\ = - 1 \times {3}^{7} \times {2}^{ - 59} \\ \\ = - \frac{ {3}^{7} }{ {2}^{59} }$

HOPE SO IT WILL HELP..