Answer :
[tex](36)v^2x^6y^{12}[/tex]
Explanation
[tex](-6vx^3y^6)^2[/tex]
Step 1
remember some properties of the exponents
[tex]\begin{gathered} (a^b)^c=a^{b\cdot c} \\ \text{for example} \\ (2^3)^4=2^{3\cdot4}=2^{12} \end{gathered}[/tex]and
[tex]\begin{gathered} (ab)^m=a^mb^m \\ \text{for example} \\ (2\cdot3)^3=2^3\cdot3^3 \end{gathered}[/tex]Step 2
then
[tex]\begin{gathered} (-6vx^3y^6)^2=(-6)^2v^2(x^3)^2(y^6)^2 \\ (-6vx^3y^6)^2=(-6\cdot-6)v^2x^{3\cdot2}y^{6\cdot2} \\ (-6vx^3y^6)^2=(36)v^2x^6y^{12} \\ (36)v^2x^6y^{12} \end{gathered}[/tex][tex]\begin{gathered} (-6vx^3y^6)^2 \\ we\text{ have a product} \\ (-6\cdot v\cdot x^3\cdot y^6)^2 \end{gathered}[/tex]and, we know
[tex](ab)^m=a^mb^m[/tex]then
[tex]\begin{gathered} (-6\cdot v\cdot x^3\cdot y^6)^2=(-6)^2\cdot(v)^{2^{}}\cdot(x^3)^2\cdot(y^6)^2 \\ =(-6)^2\cdot(v)^{2^{}}\cdot(x^3)^2\cdot(y^6)^2 \end{gathered}[/tex]and, finally
[tex]\begin{gathered} =(-6)^2\cdot(v)^{2^{}}\cdot(x^3)^2\cdot(y^6)^2=(-6\cdot-6)v^2x^6y^{12} \\ =(36)v^2x^6y^{12} \end{gathered}[/tex]I hope this helps you