Score: 0 of 1 point Multiply: $$ \left(\frac{1}{6} m^{0} n^{4}\right)\left(\frac{7}{5} m^{2} n^{3}\right)= $$ A $$ \frac{7}{30} m^{11} n^{4} $$ B $$ \frac{7}{30} m^{11} n^{7} $$ C $$ \frac{7}{30} n^{11} m^{7} $$ D $$ \frac{7}{30} m^{9} n^{7} $$

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UpStudy AI · Accepted Answer

To solve the multiplication of the two expressions $$ \left(\frac{1}{6} m^{0} n^{4}\right)\left(\frac{7}{5} m^{2} n^{3}\right) $$, we will follow these steps:

1. **Multiply the coefficients**: 
   - The coefficients are $$ \frac{1}{6} $$ and $$ \frac{7}{5} $$.
   - We multiply these together.

2. **Multiply the variables**:
   - For the variable $$ m $$, we have $$ m^{0} $$ and $$ m^{2} $$. According to the laws of exponents, $$ m^{a} \cdot m^{b} = m^{a+b} $$.
   - For the variable $$ n $$, we have $$ n^{4} $$ and $$ n^{3} $$. We will apply the same law of exponents.

Now, let's perform the calculations step by step.

### Step 1: Multiply the coefficients
$$
\frac{1}{6} \cdot \frac{7}{5} = \frac{1 \cdot 7}{6 \cdot 5} = \frac{7}{30}
$$

### Step 2: Multiply the variables
- For $$ m $$:
$$
m^{0} \cdot m^{2} = m^{0+2} = m^{2}
$$

- For $$ n $$:
$$
n^{4} \cdot n^{3} = n^{4+3} = n^{7}
$$

### Final Result
Combining the results from the coefficients and the variables, we have:
$$
\frac{7}{30} m^{2} n^{7}
$$

Now, let's check the options provided:
- A $$ \frac{7}{30} m^{11} n^{4} $$
- B $$ \frac{7}{30} m^{11} n^{7} $$
- C $$ \frac{7}{30} n^{11} m^{7} $$
- D $$ \frac{7}{30} m^{9} n^{7} $$

None of the options match $$ \frac{7}{30} m^{2} n^{7} $$.

It seems there might be a mistake in the options provided or in the interpretation of the problem. The correct answer based on the calculations is:
$$
\frac{7}{30} m^{2} n^{7}
$$
The correct answer is $$ \frac{7}{30} m^{2} n^{7} $$.

Score: 0 of 1 point Multiply: \( \left(\frac{1}{6} m^{0} n^{4}\right)\left(\frac{7}{5} m^{2} n^{3}\right)= \) A \( \frac{7}{30} m^{11} n^{4} \) B \( \frac{7}{30} m^{11} n^{7} \) C \( \frac{7}{30} n^{11} m^{7} \) D \( \frac{7}{30} m^{9} n^{7} \)

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