How do you multiply #-2u ^ { 2} v ^ { 2} \cdot ( u ^ { 4} v ^ { 4} ) ^ { 3}#?

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Answer 1 · 2017-09-06T12:28:10

See a solution process below:

First, use this rule of exponents to simplify the term on the right by eliminating the outer exponents:

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

#-2u^2v^2 * (u^color(red)(4)v^color(red)(4))^color(blue)(3) =>#

#-2u^2v^2 * u^(color(red)(4) xx color(blue)(3))v^(color(red)(4) xx color(blue)(3)) =>#

#-2u^2v^2 * u^12v^12#

Next, rewrite the expression as:

#-2(u^2 * u^12)(v^2 * v^12)#

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))#

#-2(u^color(red)(2) * u^color(blue)(12))(v^color(red)(2) xx v^color(blue)(12)) =>#

#-2u^(color(red)(2) + color(blue)(12))v^(color(red)(2) + color(blue)(12)) =>#

#-2u^14v^14#