Question

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

Answer 1

The answer is the first option

Answer 2

A.
`(8m^(7)n^(6))/(3)`

Explanation:

We have been given an exponential expression
`((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
`(1)/(x^(-n))=x^n`, we will get:

`(16m^4n^4)/(6)* m^(3)n^(2)`

`(16m^4n^4* m^(3)n^(2))/(6)`

Now, we will use exponent product property
`a^b* a^c=a^(b+c)`, we will get:

`(16m^(4+3)n^(4+2))/(6)`

`(16m^(7)n^(6))/(6)`

`(8m^(7)n^(6))/(3)`

Therefore, the expression
`(8m^(7)n^(6))/(3)` is equivalent to our given expression and option A is the correct choice.