Respuesta :

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]