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

2 Answers
May 4, 2018

Answer:

#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#

May 4, 2018

Answer:

#(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#