How do you simplify #(a^2bc)^5(a^2bc^5)#?

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Answer 1 · 2015-09-28T19:14:11

#a^12*b^6*c^10#

#(a^10*b^5*c^5)*(a^2*b*c^5)#

#(a^(10+2))(b^(5+1))(c^(5+5))#
=#a^12*b^6*c^10#

Answer 2 · 2015-09-28T19:51:51

The answer is #a^12b^6c^10# .

#(a^2bc)^5(a^2bc^5)#

Apply the exponent rule #(b^n)^m=b^(n*m)# .
.
#(a^(2*5)b^(1*5)c^(1*5))(a^2bc^5)=#

#(a^10b^5c^5)(a^2bc^5)#

Remove the parentheses and gather like terms.

#a^10a^2b^5bc^5c^5#

Apply the exponent rule #a^m*a^n=a^(m+n)#

#a^(10+2)b^(5+1)c^(5+5)=#

#a^12b^6c^10#