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

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