How do you multiply #(\frac { 2x ^ { 3} y ^ { 2} } { x ^ { 2} } ) ^ { 4} ( \frac { x ^ { 4} y ^ { 5} } { 8x ^ { 3} y ^ { 2} } )#?

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Answer 1 · 2017-02-24T04:10:48

The answer is #2x^5y^11#.

Multiply:

#((2x^3y^2)/(x^2))^4((x^4y^5)/(8x^3y^2))#

Apply the power rule of exponents #(a^m)^n=a^(m*n)#.

#((2^4x^(3*4)y^(2*4))/(x^(2*4)))((x^4y^5)/(8x^3y^2))#

Simplify.

#((16x^12y^8)/(x^8))((x^4y^5)/(8x^3y^2))#

Remove the parentheses.

#(16x^12y^8)/(x^8)(x^4y^5)/(8x^3y^2)#

Gather like terms.

#(16x^12x^4y^8y^5)/(8x^8x^3y^2)#

Apply product rule of exponents #a^ma^n=a^(m+n)#.

#(16x^(12+4)y^(8+5))/(8x^(8+3)y^2)#

Simplify.

#(2x^16y^13)/(x^11y^2)#

Apply quotient rule of exponents #a^m/a^n=a^(m-n)#.

#2x^(16-11)y^(13-2)#

Simplify.

#2x^5y^11#