Answer :
Either order is correct.
Small example: let's take [tex]n=3[/tex]. Then
[tex](x\times y)^3=(x\times y)\times(x\times y)\times(x\times y)[/tex]
By the commutative property, we can write
[tex](x\times y)^3=(x\times y)\times\underbrace{(y\times x)}\times(x\times y)[/tex]
By the associative property, we can regroup consecutive terms.
[tex](x\times y)^3=(x\times(y\times y))\times((x\times x)\times y)[/tex]
[tex](x\times y)^3=(x\times y^2)\times(x^2\times y)[/tex]
By the associative property again, we can regroup terms and write
[tex](x\times y)^3=x\times(y^2\times x^2)\times y[/tex]
Commutativity:
[tex](x\times y)^3=x\times(x^2\times y^2)\times y[/tex]
Associativity:
[tex](x\times y)^3=(x\times x^2)\times(y^2\times y)[/tex]
[tex](x\times y)^3=x^3\times y^3[/tex]
You can show by induction that this holds in general for [tex]n[/tex] so that [tex](x\times y)^n=x^n\times y^n[/tex].
Small example: let's take [tex]n=3[/tex]. Then
[tex](x\times y)^3=(x\times y)\times(x\times y)\times(x\times y)[/tex]
By the commutative property, we can write
[tex](x\times y)^3=(x\times y)\times\underbrace{(y\times x)}\times(x\times y)[/tex]
By the associative property, we can regroup consecutive terms.
[tex](x\times y)^3=(x\times(y\times y))\times((x\times x)\times y)[/tex]
[tex](x\times y)^3=(x\times y^2)\times(x^2\times y)[/tex]
By the associative property again, we can regroup terms and write
[tex](x\times y)^3=x\times(y^2\times x^2)\times y[/tex]
Commutativity:
[tex](x\times y)^3=x\times(x^2\times y^2)\times y[/tex]
Associativity:
[tex](x\times y)^3=(x\times x^2)\times(y^2\times y)[/tex]
[tex](x\times y)^3=x^3\times y^3[/tex]
You can show by induction that this holds in general for [tex]n[/tex] so that [tex](x\times y)^n=x^n\times y^n[/tex].