How do you evaluate #(- 3x ^ { 3} y ^ { 4} z ^ { 2} ) ( x y z ^ { 2} ) ( - x ^ { 5} y ^ { 2} z )#?

2 Answers
Jan 31, 2018

See a solution process below:

Explanation:

First, rearrange the expression as:

#(-3x^3y^4z^2)(xyz^2)(-x^5y^2z) =>#

#(-3x^3y^4z^2)(xyz^2)(-1x^5y^2z) =>#

#(-3 * -1)(x^3 * x * x^5)(y^4 * y * y^2)(z^2 * z^2 * z) =>#

#3(x^3 * x * x^5)(y^4 * y * y^2)(z^2 * z^2 * z)#

Next, use this rule for exponents to rewrite the expression:

#a = a^color(red)(1)#

#3(x^3 * x^color(red)(1) * x^5)(y^4 * y^color(red)(1) * y^2)(z^2 * z^2 * z^color(red)(1))#

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

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

#3(x^color(blue)(3) * x^color(red)(1) * x^color(green)(5))(y^color(blue)(4) * y^color(red)(1) * y^color(green)(2))(z^color(blue)(2) * z^color(green)(2) * z^color(red)(1)) =>#

#3x^(color(blue)(3)+color(red)(1)+color(green)(5))y^(color(blue)(4)+color(red)(1)+color(green)(2))z^(color(blue)(2)+color(green)(2)+color(red)(1)) =>#

#3x^9y^7z^5#

Jan 31, 2018

#3x^9y^7z^5#

Explanation:

Take each different term and multiply them. Powers multiply by adding the exponents.
#-3*-1=3#
#x^3*x^1*x^5=x^9#
#y^4*y^1*y^2=y^7#
#z^2*z^2*z^1=z^5#