To simplify this expression, we first need to expand the cube of the binomial (3b^2c)^4 using the power of a power rule:
(3b^2c)^4 = 3^4 (b^2)^4 c^= 81 b^8 c^4
Now, we substitute this back into the original expression:
-81b^6c^3 / (3b^2c)^= -81b^6c^3 / (81b^8c^4)
Now, we can simplify this expression by dividing each term in the numerator by the corresponding term in the denominator:
= -1/b^2
Therefore, the simplified expression is -1/b^2.
To simplify this expression, we first need to expand the cube of the binomial (3b^2c)^4 using the power of a power rule:
(3b^2c)^4 = 3^4 (b^2)^4 c^
= 81 b^8 c^4
Now, we substitute this back into the original expression:
-81b^6c^3 / (3b^2c)^
= -81b^6c^3 / (81b^8c^4)
Now, we can simplify this expression by dividing each term in the numerator by the corresponding term in the denominator:
= -1/b^2
Therefore, the simplified expression is -1/b^2.