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

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Answer 1 · 2018-04-03T07:41:35

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

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:

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

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

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