How do you multiply #(a c ) ^ { 4} \cdot ( a b c ) ^ { 12} \cdot ( b c ) ^ { 5} \cdot ( a b ) ^ { 8}#?

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Answer 1 · 2017-04-22T00:42:57

#(ac)^4(abc)^12(bc)^5(ab)^8=color(blue)(a^24b^25c^21#

Multiply:

#(ac)^4(abc)^12(bc)^5(ab)^8#

Apply the multiplication distributive property, #(xy)^n=x^ny^n#.

#(a^4c^4)(a^12b^12c^12)(b^5c^5)(a^8b^8)#

Group like terms.

#(a^4*a^12*a^8)(b^12*b^5*b^8)(c^4*c^12*c^5)#

Apply the product rule, #x^m*x^n=x^(m+n)#.

#(a^(4+12+8))(b^(12+5+8))(c^(4+12+5))#

Simplify.

#(a^24)(b^25)(c^21)#

Remove parentheses.

#a^24b^25c^21#