Question

simplify the following

Answer 1

Identities used :

${a}^{m} \times {a}^{n} = {a}^{ m+ n} \\ \\ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{ m-n } \\ \\ ( {a}^{m} )^{n} = {a}^{mn}$

Now,

$- \frac{ {a}^{ - 3} {b}^{10} {c}^{8} \times b {c}^{8} }{ ({b}^{ - 10} \times {c}^{6})^ {4} } \\ \\ = - \frac{ {a}^{ - 3} {b}^{10 + 1} {c}^{8 + 8} }{ {b}^{ - 10 \times 4} {c}^{6 \times 4} } \\ \\ = - \frac{ {a}^{ - 3} {b}^{11} {c}^{16} }{ {b}^{ - 40} {c}^{24} } \\ \\ = - {a}^{ - 3} {b}^{11 - ( - 40)} {c}^{16 - 24} \\ \\ = - {a}^{ - 3} {b}^{51} {c}^{ - 8} \\ \\ = \bf - \frac{ {b}^{51} }{ {a}^{3} {c}^{8} }$

Hopw it helps! ;)