Question

Simplify the expression completely.

(3mn2)2(2m0n)3(3𝑚𝑛2)2(2𝑚0𝑛)3

(1 point)

$$mn

Please choose an answer.

Answer 1

To simplify the expression \((3mn^2)^2(2m^0n)^3(3mn^2)^2(2m^0n)^3\), we will first simplify each part step by step:

1. **First term: \((3mn^2)^2\)**:
\[
(3mn^2)^2 = 3^2 \cdot m^2 \cdot (n^2)^2 = 9m^2n^4
\]

2. **Second term: \((2m^0n)^3\)**:
Since \(m^0 = 1\):
\[
(2m^0n)^3 = (2 \cdot 1 \cdot n)^3 = 2^3 \cdot n^3 = 8n^3
\]

3. **Third term: \((3mn^2)^2\)** (same as first term):
\[
(3mn^2)^2 = 9m^2n^4
\]

4. **Fourth term: \((2m^0n)^3\)** (same as second term):
\[
(2m^0n)^3 = 8n^3
\]

Now we can combine all the simplified terms together:
\[
(9m^2n^4) \cdot (8n^3) \cdot (9m^2n^4) \cdot (8n^3)
\]

First, calculate the coefficients:
\[
9 \cdot 8 \cdot 9 \cdot 8 = 576
\]

Next, combine the variables:
- For \(m\):
\[
m^2 \cdot m^2 = m^{2+2} = m^4
\]

- For \(n\):
\[
n^4 \cdot n^3 \cdot n^4 \cdot n^3 = n^{4+3+4+3} = n^{14}
\]

Thus, we have:
\[
576m^4n^{14}
\]

So, the fully simplified expression is:
\[
\boxed{576m^4n^{14}}
\]