How would you solve 4m(-2mn^2)^3/4m^-6n4.

In addition, what steeps are required

Nothing to solve. If you mean to simplify it, then

4m(-2mn^2)^3 / 4m^-6n4
= 4m(-8m^3n^6) / 4m^-6n^4
= -32m^4n^6 / 4m^-6n^4
= -8m^10n^2

Thank you Steve

To solve the expression 4m(-2mn^2)^3/4m^-6n^4, we need to simplify it step by step using the rules of exponents and order of operations.

1. First, let's simplify the expression inside the parentheses (-2mn^2)^3. Applying the exponent to every term inside, we have -2^3 * m^3 * n^2^3, which simplifies to -8m^3n^6.

2. Now we can substitute this simplified result back into the original expression: 4m * (-8m^3n^6) / 4m^-6n^4.

3. Next, we apply the rule of division with exponents: when dividing with the same base, we subtract the exponents. So, for m, we have m^1 (since 1 - (-6) = 7). For n, we have n^(-6 - 4) = n^(-10).

4. After applying the exponent rule, we simplify further: 4m * (-8m^3n^6) / (4m^7n^-10).

5. Now, let's simplify the multiplication of the coefficients: 4 * (-8) = -32.

6. Continuing with the simplification, we combine the variables: m * m^3 * m^7 = m^(1 + 3 + 7) = m^11. Similarly, n^6 * n^(-10) = n^(6 + -10) = n^(-4).

7. We now have: -32m^11 / n^(-4).

8. Finally, using the rule of negative exponents, we move the term with a negative exponent to the denominator: -32m^11n^4.

To summarize the steps required:
1. Simplify the expression inside the parentheses using the exponent.
2. Substitute the simplified result back into the original expression.
3. Apply the rule of division with exponents and simplify further.
4. Perform the multiplication of the coefficients.
5. Combine the variables by adding their exponents.
6. Simplify the exponents further.
7. Write the final expression.