Question

((-6 *v*( x to the third power) *(y to the 6 power)) 2 square

Answer 1

`(36)v^2x^6y^(12)`

Step-by-step explanation

`(-6vx^3y^6)^2`

Step 1

remember some properties of the exponents

`\begin{gathered} (a^b)^c=a^(b\cdot c) \\ \text{for example} \\ (2^3)^4=2^(3\cdot4)=2^(12) \end{gathered}`

and

`\begin{gathered} (ab)^m=a^mb^m \\ \text{for example} \\ (2\cdot3)^3=2^3\cdot3^3 \end{gathered}`

Step 2

then

`\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}`
`\begin{gathered} (-6vx^3y^6)^2 \\ we\text{ have a product} \\ (-6\cdot v\cdot x^3\cdot y^6)^2 \end{gathered}`

and, we know

`(ab)^m=a^mb^m`

then

`\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}`

and, finally

`\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}`

I hope this helps you