Raise each factor within the parentheses to the -4 power and simplify to positive exponents: (-4 m^-2 n^11)^-4.

Step-by-step solution

1. 1

   Distribute the outer exponent to every factor, the numerical one included. The rule $(abc)^{k}=a^{k}b^{k}c^{k}$ applies to the coefficient $-4$ just as much as to the variables — leaving the coefficient untouched is the usual mistake here:

   $\left(-4\,m^{-2}n^{11}\right)^{-4}=(-4)^{-4}\left(m^{-2}\right)^{-4}\left(n^{11}\right)^{-4}$

2. 2

   Evaluate the numerical factor and watch the sign. A negative exponent means a reciprocal, and the base $-4$ is raised to an even power, so the result is positive:

   $(-4)^{-4}=\frac{1}{(-4)^{4}}=\frac{1}{256}$

   Had the exponent been odd, the sign would have survived.

3. 3

   Multiply the variable exponents. Using $\left(a^{p}\right)^{q}=a^{pq}$, and remembering that a negative times a negative is positive:

   $\left(m^{-2}\right)^{-4}=m^{(-2)(-4)}=m^{8},\qquad \left(n^{11}\right)^{-4}=n^{11(-4)}=n^{-44}$

   So the expression is now $\dfrac{1}{256}\,m^{8}n^{-44}$.

4. 4

   Move the remaining negative exponent into the denominator. Since $n^{-44}=\dfrac{1}{n^{44}}$,

   $\frac{1}{256}m^{8}n^{-44}=\frac{m^{8}}{256\,n^{44}}$

   Every exponent is now positive, which is the requested form.

5. 5

   Check numerically. At $m=1.7$ and $n=0.9$ the original expression evaluates to $28.098361160882813$, and $\dfrac{m^{8}}{256\,n^{44}}$ gives the identical $28.098361160882813$. The agreement to full precision confirms both the sign and all three exponents.