Question

Simplify the expression.

Answer 1

The third one I guess

Answer 2

Answer:

$9x^8y^{12}$

Step-by-step 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