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

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Answer 1 · 2017-07-05T12:57:06

See a solution process below:

First, use this rule of exponents to eliminate the outer exponent for the term on the left:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(-y^color(red)(3)z^color(red)(3))^color(blue)(3)(x^4y^2z^3) =>#

#(-y^(color(red)(3)xxcolor(blue)(3))z^(color(red)(3)xxcolor(blue)(3)))(x^4y^2z^3) =>#

#(-y^9z^9)(x^4y^2z^3)#

Next, rewrite the expression as:

#x^4(-y^9y^2)(z^9z^3)#

Now, use this rule of exponents to complete the multiplication:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#x^4(-y^color(red)(9)y^color(blue)(2))(z^color(red)(9)z^color(blue)(3)) =>#

#x^4(-y^(color(red)(9)+color(blue)(2)))z^(color(red)(9)+color(blue)(3)) =>#

#x^4(-y^11)z^12 =>#

#-x^4y^11z^12 =>#

Answer 2 · 2017-07-05T13:06:09

#-x^4y^11z^12#

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

#;.=-y^9z^9*x^4y^2z^3#

#:.=-y^(9+2)z^(9+3)x^4#

#:.=-x^4y^11z^12#