We have to simplify: (2a^3 b^-3 c^-1 / 3a^-2 b^-2 c^3)^3
(2a^3 b^-3 c^-1 / 3a^-2 b^-2 c^3)^3
The required simplified form is (8/27)*a^15/(b^3*c^12)
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.
The entire fraction, both numerator and denominator, is raised to the 3rd power.
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)