Answer:
1:
[tex] {( - 6)}^{2} \times {( - 6)}^{5} [/tex]
from law of indices:
[tex] {a}^{n} \times {a}^{m} = {a}^{(n + m)} [/tex]
therefore:
[tex] = ( - 6) {}^{ \{2 + 5 \}} \\ = ( - 6) {}^{7} \\ = { \boxed{ \boxed{ - 279936}}}[/tex]
2:
[tex] - 4 {a}^{5} (6 {a}^{5} ) \\ = ( - 4 \times 6)( {a}^{5} \times {a}^{5} ) \\ = - 24 \{{a}^{(5 + 5)} \} \\ = { \boxed{ \boxed{ - 24 {a}^{10} }}}[/tex]
3:
[tex]( - 7 {a}^{4} b {c}^{3} )(5a {b}^{4} {c}^{2} ) \\ = ( - 7 \times 5)( {a}^{4} \times a)(b \times {b}^{4}) \times ( {c}^{3} \times {c}^{2} ) \\ = - 35 {a}^{5} {b}^{5 } {c}^{5} \\ = { \boxed{ \boxed{ - 35 {(abc)}^{5} }}}[/tex]
4:
[tex] \frac{ {8}^{15} }{ {8}^{13} } [/tex]
from law of indices:
[tex] \frac{a {}^{n} }{ {a}^{m} } = {a}^{(n - m) } \\ [/tex]
therefore:
[tex] = {8}^{(15 - 13)} \\ { \boxed{ \boxed{ {8}^{2} = 64 }}}[/tex]
follow the procedure for application to other questions.
Any question, be free to ask. Thank you …
