Question

Simplify the expression.

(3xy3)2(xy)6


3x8y12


9x8y9


2x3y12


9x8y12

Answer 1

The third one I guess

Answer 2

`9x^8y^(12)`

Explanation:

The expression is:

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

we use the following rule to simplify the expression:

`(a^m)^n=a^(m*m)`

that is, we multiply the exponent inside the parentheses by the exponent outside the parentheses (also using
`x=x^1`):

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

and we simplify the exponents and substitute
`3^2=9`:

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

We have not finished simplifying yet, since we have that x and y are repeated we must use the following law of exponents:

`a^ma^n=a^(m+n)`

We add the exponents that each variable has.

thus, the expression becomes:

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

and we simplify the exponents:

`9x^8y^(12)`

which is the fourth option