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

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Answer 1 · 2017-03-26T03:04:20

#(-3x^3yz^4)^2(3y^2z^2) = 27x^6y^4z^10#

Given: #(-3x^3yz^4)^2(3y^2z^2)#

Watch out for expressions like this one - it is easy to miss the #( ... ) ^2# and jump into multiplying the first term by the second.

This expression should be written out as follows as a first step:

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

Then the expression can clearly be solved by multiplying all the numeric values, and adding all the #like# exponents.

#-3*-3*3 = 27; x^3*x^3 = x^6; y*y*y^2 = y^4; z^4*z^4*z^2 = z^10 #

And putting it all together:

#(-3x^3yz^4)^2(3y^2z^2) = 27x^6y^4z^10#