Question

dividing monomials
( 2m^4n^2)^3
( 4m^2n)

Answer 1

To divide the monomials \((2m^4n^2)^3\) by \((4m^2n)\), we'll follow these steps:

1. **Calculate \((2m^4n^2)^3\)**:
- Raise the coefficient and each variable to the power of 3:
\[
(2^3)(m^{4 \cdot 3})(n^{2 \cdot 3}) = 8m^{12}n^6
\]

2. **Write down the expression to divide**:
\[
\frac{8m^{12}n^6}{4m^2n}
\]

3. **Divide the coefficients**:
\[
\frac{8}{4} = 2
\]

4. **Divide the \(m\) terms**:
\[
\frac{m^{12}}{m^2} = m^{12-2} = m^{10}
\]

5. **Divide the \(n\) terms**:
\[
\frac{n^6}{n^1} = n^{6-1} = n^{5}
\]

6. **Combine the results**:
\[
2m^{10}n^5
\]

So, the final result of dividing \((2m^4n^2)^3\) by \((4m^2n)\) is:
\[
\boxed{2m^{10}n^5}
\]