Answer:
[tex]m=3^{-12}[/tex]
Step-by-step explanation:
we are given that
[tex]\frac{9m}{3^{-2}}=9^{-4}[/tex]
[tex]\frac{3^{2}\times m}{3^{-2}}=(3^{2})^{-4}[/tex]
applying the rule of exponents
[tex](m^{a})^{b}=m^{ab}[/tex]
[tex]{3^{2}\times m=3^{-8} \times 3^{-2}[/tex]
[tex]m=\frac{3^{-8} \times 3^{-2}}{3^{2}}[/tex]
applying the rule of exponents
[tex]\frac{1}{m^a}=m^{-a}[/tex]
[tex]m=3^{-8} \times 3^{-2}\times 3^{-2}[/tex]
[tex]m=3^{-8-2-2}[/tex]
[tex]m=3^{-12}[/tex]
[tex]m=\frac{1}{3^{12}}[/tex]