How do you multiply #(- 4a ) ( - 7b ^ { 2} c ^ { 2} ) ( - 2a c ^ { 3} d ^ { 3} )#?

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Answer 1 · 2018-03-15T13:20:57

See a solution process below:

First, rewrite the expression as:
#(-4 * -7 * -2)(a * a)b^2(c^2 * c^3)d^3 =>#

#-56(a * a)b^2(c^2 * c^3)d^3#

Next, use this rule for exponents to rewrite the #a# terms:

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

#-56(a^1 * a^1)b^2(c^2 * c^3)d^3#

Now, use this rule of exponents to multiply the #a# and #c# terms:

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

#-56(a^color(red)(1) * a^color(blue)(1))b^2(c^color(red)(2) * c^color(blue)(3))d^3 =>#

#-56a^(color(red)(1)+color(blue)(1))b^2c^(color(red)(2)+color(blue)(3))d^3 =>#

#-56a^2b^2c^5d^3#