Question

Which expression is equivalent to StartFraction (3 m Superscript negative 2 Baseline n) Superscript negative 3 Baseline Over 6 m n Superscript negative 2 Baseline EndFraction? Assume m not-equals 0, n not-equals 0.
StartFraction m Superscript 5 Baseline Over 162 n EndFraction
StartFraction 1 Over 2 m cubed n EndFraction
StartFraction 8 m Superscript 9 Baseline Over n Superscript 9 Baseline EndFraction
StartFraction 4 m Superscript 8 Baseline Over 3 n cubed EndFraction

Answer 1

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.

Answer 2

Answer:

D

Step-by-step explanation: