Option a:
is the equivalent expression.
Explanation:
The expression is
where ![m\neq 0, n\neq 0](https://tex.z-dn.net/?f=m%5Cneq%200%2C%20n%5Cneq%200)
Let us simplify the expression, to determine which expression is equivalent from the four options.
Multiplying the powers, we get,
![\frac{3^{-3}m^{6} n^{-3}}{6mn^{-2} }](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B-3%7Dm%5E%7B6%7D%20n%5E%7B-3%7D%7D%7B6mn%5E%7B-2%7D%20%7D)
Cancelling the like terms, we have,
![\frac{3^{-3}m^{5} n^{-1}}{6 }](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B-3%7Dm%5E%7B5%7D%20n%5E%7B-1%7D%7D%7B6%20%7D)
This equation can also be written as,
![\frac{m^{5}}{3^{3}6 n^{1} }](https://tex.z-dn.net/?f=%5Cfrac%7Bm%5E%7B5%7D%7D%7B3%5E%7B3%7D6%20n%5E%7B1%7D%20%7D)
Multiplying the terms in denominator, we have,
![\frac{m^{5} }{162n}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%5E%7B5%7D%20%7D%7B162n%7D)
Thus, the expression which is equivalent to
is ![\frac{m^{5} }{162n}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%5E%7B5%7D%20%7D%7B162n%7D)
Hence, Option a is the correct answer.