Answer:
see explanation
Step-by-step explanation:
Using the rules of exponents
All the exponents inside the parenthesis are multiplied by the exponent outside the parenthesis.
Then
[tex]\frac{m^{-7}n^{14} }{m^{-25}n^{40} }[/tex] ÷ [tex]\frac{m^{-21}n^{42} }{m^{-25}n^{40} }[/tex]
[ Using the rule [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] ]
= [tex]m^{(-7-14)}[/tex] [tex]n^{(14-(-28)}[/tex] ÷ [tex]m^{(-15-10)}[/tex] [tex]n^{(25-(-15)}[/tex]
= [tex]m^{-21}[/tex] [tex]n^{14+28}[/tex] ÷ [tex]m^{-25}[/tex] [tex]n^{25+15}[/tex]
= [tex]\frac{m^{-21}n^{42} }{m^{-25}n^{40} }[/tex]
= [tex]m^{(-21-(-25))}[/tex] [tex]n^{(42-40)}[/tex]
= [tex]m^{(-21+25)}[/tex] n²
= [tex]m^{4}[/tex] n² = [tex]m^{x}[/tex] [tex]n^{y}[/tex] , so x = 4 and y = 2
Then
[tex]m^{x-2y}[/tex] = [tex]m^{4-2(2)}[/tex] = [tex]m^{4-4}[/tex] = [tex]m^{0}[/tex] = 1 ← as required
