How do you simplify #(-7ab^4c)^3[(2a^2c)^2]^3#?

1 Answer
Apr 3, 2018

Answer:

#-21952a^15b^12c^9#

Explanation:

First of all, let's work with the powers of the round brackets: the power of a product is the power of each single factor

#(-7ab^4c)^3 = (-7)^3 * a^3 * b^(4*3) * c^3 = -343a^3b^12c^3#

In the same fashion,

#(2a^2c)^2 = 2^2*a^(2*2)c^2 = 4a^4c^2#

So, we have

#(-343a^3b^12c^3) * (4a^4c^2)^3#

Again, we have to cube the last parenthesis:

#(4a^4c^2)^3 = 4^3 * a^(4*3)c^(2*3) = 64a^12c^6#

Finally, we multiply the two parenthesis:

#(-343a^3b^12c^3)(64a^12c^6)#

Now we multiply similar factors:

#-343*64 a^(3+12)b^12c^(3+6)#

#-21952a^15b^12c^9#