Question

Which expression is equivalent to (2mn)^4/6m^-3n^-2? Assume .m=0,n=0

8m^7n^6/3
10m^7n^6/3
8m^16n^12/3
m^4n^6/3

Answer 1

8m^7n^6
------------
3

Answer 2

Given expression:
`((2mn)^4)/(6m^(-3)n^(-2))`.

`\mathrm{Apply\:exponent\:rule}:\quad \left(ab\right)^c=a^cb^c`

`\left(2mn\right)^4:\quad 2^4m^4n^4`

`=(2^4m^4n^4)/(6m^(-3)n^(-2))`

`=(2^4m^4n^4)/(2\cdot \:3m^(-3)n^(-2))`

`=(2^3m^4n^4)/(3m^(-3)n^(-2))`

`\mathrm{Apply\:exponent\:rule}:\quad (x^a)/(x^b)\:=\:x^(a-b)`

`(m^4)/(m^(-3))=m^(4-\left(-3\right))=m^7`

`=(2^3m^7n^4)/(3n^(-2))`

`(n^4)/(n^(-2))=n^(4-\left(-2\right))=n^6`

`=(2^3m^7n^6)/(3)`

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

Therefore, correct option is first option
`(8m^7n^6)/(3).`