Express the following in simplified form without zero and negative exponents (2a^3 b^-3 c^-1 / 3a^-2 b^-2 c^3)^3Show complete solution to explain...

According to exponential law, when powers are divided,
their exponents are subtracted.

n^a / n^b =
n^a-b

Take a look at each variable by itself.  Subtract the
exponents.  Remember that minus negative becomes
addition.

a^3 / a^-2 = a^(3 - -2) =
a^5

b^-3 / b^-2 = b^(-3 - -2) =
b^-1

c^-1 / c^3 = c^(-1 - 3) =
c^-4

The variables with positive exponents will be part of
the numerator and the variables with negative exponents will be part of the
denominator.

numerator: 
2a^5

denominator:  3b^1c^4

The
entire fraction, both numerator and denominator, is raised to the 3rd
power.

numerator:
(2a^5)^3

denominator:
(3b^1c^4)^3

According to exponential law, to find the power
of a power, you multiply the exponents.  Remember to also distribute the exponent 3 to
the contants.

numerator:  2^3 * a^(5*3) =
8a^15

denominator:  3^3 * b^(1*3) * c^(4*3) =
27b^3c^12

The final simplified answer
is...

(8a^15) /
(27b^3c^12)