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

1 Answer
smendyka
Jul 23, 2017

See a solution process below:

Explanation:

First, use these rules for exponents to simplify the term on the left of the expression:

#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#(-3x^4yz^2)^2(x^3z^2) => (-3^color(red)(1)x^color(red)(4)y^color(red)(1)z^color(red)(2))^color(blue)(2)(x^3z^2) =>#

#(-3^(color(red)(1) xx color(blue)(2))x^(color(red)(4) xx color(blue)(2))y^(color(red)(1) xx color(blue)(2))z^(color(red)(2) xx color(blue)(2)))(x^3z^2) =>#

#(-3^2x^8y^2z^4)(x^3z^2) =>#

#(9x^8y^2z^4)(x^3z^2)#

Next, rewrite the expression as:

#9(x^8 * x^3)y^2(z^4 * z^2)#

Now, this rule of exponents to multiply the #x# and #z# terms:

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

#9(x^color(red)(8) * x^color(blue)(3))y^2(z^color(red)(4) * z^color(blue)(2)) =>#

#9x^(color(red)(8)+color(blue)(3))y^2z^(color(red)(4)+color(blue)(2)) =>#

#9x^11y^2z^6#

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