How do you multiply #(- x ^ { 2} y ^ { 2} z ^ { 4} ) ^ { 5} \cdot - y ^ { 2} z ^ { 2}#?

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Answer 1 · 2017-02-06T01:32:57

#(-x^2y^2z^4)^5*-y^2z^2# multiplied equals #x^10y^12z^22#.

Multiply #(-x^2y^2z^4)^5*-y^2z^2#.

A negative times a negative gives a positive result, so the minus signs can be removed.

#(x^2y^2z^4)^5*y^2z^2#

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

#(x^(2*5)y^(2*5)z^(4*5))y^2z^2#

Simplify.

#x^10y^10z^20y^2z^2#

Group like terms. and apply product rule #a^ma^n=a^(m+n)#.

#x^10y^10y^2z^(20)z^2#

Simplify.

#x^10y^((10+2))z^((20+2))#

Simplify.

#x^10y^12z^22#