Question

Whats the answer hurry !!

Answer 1

Answer:

$=\frac{81m^2n^5}{8}$

Step-by-step explanation:

One is given the following expression:

$\frac{(3m^-^1n^2)^4}{(2m^-^2n)^3}$

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:

$=\frac{(3m^-^1n^2)^4}{(2m^-^2n)^3}$

$=\frac{3^4m^(^-^1^)^(^4^)n^(^2^)^(^4^)}{2^3m^(^-^2^)^(^3^)n^3}$

$=\frac{81m^-^4n^8}{8m^-^6n^3}$

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:

$=\frac{81m^-^4n^8}{8m^-^6n^3}$

$=\frac{81m^(^-^4^)^-^(^-^6^)n^(^8^)^-^(^3^)}{8}$

$=\frac{81m^-^4^+^6n^8^-^3}{8}$

$=\frac{81m^2n^5}{8}$