Question

Which expression is equivalent to (2mn)^4/6m^-3n^-2

Answer 1

The answer is the first option

Answer 2

Answer:

A. $\frac{8m^{7}n^{6}}{3}$

Step-by-step explanation:

We have been given an exponential expression $\frac{(2mn)^4}{6m^{-3}n^{-2}}$.

We will use exponent properties to solve our given problem.

Using property $(ab)^c=a^cb^c$, we will get:

$(2mn)^4=2^4*m^4n^4=16m^4n^4$

Using property $\frac{1}{x^{-n}}=x^n$, we will get:

$\frac{16m^4n^4}{6}\times m^{3}n^{2}$

$\frac{16m^4n^4\times m^{3}n^{2}}{6}$

Now, we will use exponent product property $a^b\times a^c=a^{b+c}$, we will get:

$\frac{16m^{4+3}n^{4+2}}{6}$

$\frac{16m^{7}n^{6}}{6}$

$\frac{8m^{7}n^{6}}{3}$

Therefore, the expression $\frac{8m^{7}n^{6}}{3}$ is equivalent to our given expression and option A is the correct choice.