Question

Which expression is equivalent to (3m^-1 * n^2)^-4 / (2m^-2 * n)^3?

a) 2m^2 * n^5
b) 81m^2 * n^5 / 8
c) 2m^2 * n^2
d) 81m^2 * n^2 / 8

Answer 1

The expression equivalent to (3m^-1 * n^2)^-4 / (2m^-2 * n)^3 is 81m^2 * n^2 / 8.

Step-by-step explanation:

To simplify the given expression, we need to apply the exponent rules which state that when we raise a product or quotient to a power, we can distribute the power to each term inside the parentheses. Let's simplify step by step:

(3m-1 * n2)-4 / (2m-2 * n)3

Using the power rule, we obtain:

(1/(3m*n2)4) / ((2m-2 * n)3)

Now, applying the power rule again, we get:

1/((34 * m4 * n8) / (23 * m-6 * n3))

Simplifying further, we have:

1/((81m4 * n8) / (8m-6 * n3))

Finally, by multiplying the numerator and denominator by their common denominator, we get:

(8m-6 * n3) / (81m4 * n8) = 81m2 * n2 / 8