Answer:
m = - 15
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then
[tex](-\frac{3}{4}) ^{-4}[/tex] × [tex](-\frac{3}{4}) ^{-11}[/tex] = [tex](-\frac{3}{4}) ^{m}[/tex] , that is
[tex](-\frac{3}{4}) ^{(-4-11)}[/tex] = [tex](-\frac{3}{4}) ^{m}[/tex]
[tex](-\frac{3}{4}) ^{-15}[/tex] = [tex](-\frac{3}{4}) ^{m}[/tex]
Equating exponents gives
m = - 15
