Answer:
Option a: \frac{m^{5} }{162n} is the equivalent expression.
Explanation:
The expression is \frac{(3m^{-2} n)^{-3}}{6mn^{-2} } where m\neq 0, n\neq 0
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} }
Cancelling the like terms, we have,
\frac{3^{-3}m^{5} n^{-1}}{6 }
This equation can also be written as,
\frac{m^{5}}{3^{3}6 n^{1} }
Multiplying the terms in denominator, we have,
\frac{m^{5} }{162n}
Thus, the expression which is equivalent to \frac{(3m^{-2} n)^{-3}}{6mn^{-2} } is \frac{m^{5} }{162n}
Hence, Option a is the correct answer. 23
Step-by-step explanation:
