How do you simplify (a^2bc)^5(a^2bc^5)(a2bc)5(a2bc5)?

2 Answers
Sep 28, 2015

a^12*b^6*c^10a12b6c10

Explanation:

(a^10*b^5*c^5)*(a^2*b*c^5)(a10b5c5)(a2bc5)

(a^(10+2))(b^(5+1))(c^(5+5))(a10+2)(b5+1)(c5+5)
=a^12*b^6*c^10a12b6c10

Sep 28, 2015

The answer is a^12b^6c^10a12b6c10 .

Explanation:

(a^2bc)^5(a^2bc^5)(a2bc)5(a2bc5)

Apply the exponent rule (b^n)^m=b^(n*m)(bn)m=bnm .
.
(a^(2*5)b^(1*5)c^(1*5))(a^2bc^5)=(a25b15c15)(a2bc5)=

(a^10b^5c^5)(a^2bc^5)(a10b5c5)(a2bc5)

Remove the parentheses and gather like terms.

a^10a^2b^5bc^5c^5a10a2b5bc5c5

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

a^(10+2)b^(5+1)c^(5+5)=a10+2b5+1c5+5=

a^12b^6c^10a12b6c10