How do you simplify #(- 2x ^ { 3} y ^ { 2} ) ^ { 4} ( 4x ^ { 3} y ^ { 3} ) ^ { 2}#?

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Answer 1 · 2017-10-16T00:44:30

#(-2x^3y^2)^4(4x^3y^3)^2=color(blue)(256x^18y^14#

Simplify:

#(-2x^3y^2)^4(4x^3y^3)^2#

Apply the exponent power rule: #(a^m)^n=a^(m*n)#.

#(-2^4x^(3*4)y^(2*4))(4^2x^(3*2)y^(3*2))#

Simplify.

#(16x^12y^8)(16x^6y^6)#

Gather like terms.

#(16*16)(x^12x^6)(y^8y^6)#

Simplify.

#256(x^12x^6)(y^8y^6)#

Apply the product rule: #a^m^n=a^(m+n)#.

#256(x^(12+6)y^(8+6)#

Simplify.

#256x^18y^14#