Question

Whats the answer hurry !!

Answer 1

`=(81m^2n^5)/(8)`

Explanation:

One is given the following expression:

`((3m^-^1n^2)^4)/((2m^-^2n)^3)`

Simplify, distribute the exponent outside of the parenthesis by the terms inside of it. Remember, when a value that already has an exponent is raised to another exponent, the equivalent of these two values is multiplying the exponents together. Use this property here:

`=((3m^-^1n^2)^4)/((2m^-^2n)^3)`

`=(3^4m^(^-^1^)^(^4^)n^(^2^)^(^4^))/(2^3m^(^-^2^)^(^3^)n^3)`

`=(81m^-^4n^8)/(8m^-^6n^3)`

Now simplify this fraction. Keep in mind that a fraction is another way of representing the operation of division. When one wants to divide terms raised to an exponent, one must make sure that these terms have a like base. Then one will subtract the exponents from each other. Do this step with terms that have a variable base:

`=(81m^-^4n^8)/(8m^-^6n^3)`

`=(81m^(^-^4^)^-^(^-^6^)n^(^8^)^-^(^3^))/(8)`

`=(81m^-^4^+^6n^8^-^3)/(8)`

`=(81m^2n^5)/(8)`