Simplifying expressions

[RHSLilSweetie07]

Simplify the following:

(abc)^4*(4b)^-2*(3a)^3

Am I correct in assuming that (abc)^4 is equal to a^4*b^4*c^4?

[(a^4*b^4*c^4)*(3a)^3]/(4b)^2
[(a^4*b^4*c^4)*27a^3]/[16b^2]
[27*a^7*b^4*c^4]/[16*b^2]
[27*a^7*b^2*c^4]/16

Is this all correct? Is it completely simplified? Please help.

 

[Unco]

Simplify the following:

$\displaystyle (abc)^4\times(4b)^{-2}\times(3a)^3$

Am I correct in assuming that $\displaystyle (abc)^4$ is equal to $\displaystyle a^4\times b^4\times c^4$? ... That's a fact!

$\displaystyle \frac{(a^4b^4c^4)(3a)^3}{(4b)^2}$

$\displaystyle \frac{(a^4b^4c^4)27a^3}{16b^2}$

$\displaystyle \frac{27a^7b^4c^4}{16b^2}$

$\displaystyle \frac{27a^7b^2c^4}{16}$

Is this all correct? Is it completely simplified? ... looks perfect to me, impressive work!