Here are a few rules with exponents that apply here:
- Raising a power to a power: [tex](x^m)^n=x^{m*n}[/tex]
- Dividing exponents of the same base: [tex]\frac{x^m}{x^n}=x^{m-n}[/tex]
- Converting negative exponents to positive ones: [tex]x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m[/tex]
Firstly, solve the outer exponent:
[tex](\frac{4mn}{m^{-2}n^{6}})^{-2}=\frac{4^{-2}m^{-2}n^{-2}}{m^{-2*-2}n^{6*-2}}=\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}[/tex]
Next, divide:
[tex]\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}=4^{-2}m^{-2-4}n^{-2-(-12)}=4^{-2}m^{-6}n^{10}[/tex]
Next, convert the negative exponents:
[tex]4^{-2}m^{-6}n^{10}=\frac{n^{10}}{4^2m^6}=\frac{n^{10}}{16m^6}[/tex]
Your final answer is n^10/16m^6 , or B.
