ANSWER
[tex]\boxed {} = {x}^{158} [/tex]
EXPLANATION
The given expression is:
[tex] ({ {x}^{12} )}^{5} \times ({ {x}^{ - 2} )}^{9} \boxed {} = ({ {x}^{40} )}^{5} [/tex]
Use the property,
[tex]({ {a}^{m} )}^{n} = { {a}^{mn} }[/tex]
[tex]({ {x}^{60} )} \times ({x}^{ - 18} )\boxed {} = ({ {x}^{200} )}[/tex]
Use the property,
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
[tex]({ {x}^{60 + - 18} )} \boxed {} = ({ {x}^{200} )}[/tex]
[tex]({ {x}^{42} )} \boxed {} = ({ {x}^{200} )}[/tex]
Solve for box,
[tex]\boxed {} = \frac{{x}^{200} }{{x}^{42}} [/tex]
Since they are dividing we subtract the exponents:
[tex]\boxed {} = {x}^{200 - 42} = {x}^{158} [/tex]
