Question

How do you simplify `(3xy^3)^2(xy)^6`?

Answer 1

`9x^8y^12`

Explanation:

`(3xy^3)^2(xy)^6`

This can also be written (for simplicity of understanding) as:

`(3^1x^1y^3)^2(x^1y^1)^6`

We first open the brackets separately and simplify them by multiplying the exponential power outside the bracket with each individual power inside the bracket.

`(3^2x^2y^6)(x^6y^6)`

Since `3^2` is `9` we write that:

`(9x^2y^6)(x^6y^6)`

Now we combine both brackets by opening them and multiplying the like terms with each other by adding their respective powers:

`9x^8y^12`

Answer 2

`(3xy^3)^2(xy)^6=color(blue)(9x^8y^12`

Explanation:

Simplify:

`(3xy^3)^2(xy)^6`

Apply multiplication distributive property: `(ab)^m=a^mb^m`

`3^2x^2(y^3)^2x^6y^6`

Apply power rule of exponents: `(a^m)^n=a^(m*n)`

`3^2x^2y^(3*2)x^6y^6`

Simplify `3^2` to `9`.

`9x^2y^(3*2)x^6y^6`

Simplify `y^(3*2)` to `y^6`.

`9x^2y^6x^6y^6`

Regroup variables.

`9x^2x^6y^6y^6`

Apply product rule of exponents: `a^ma^n=a^(m+n)`

`9x^(2+6)y^(6+6)`

`9x^8y^12`