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 \( \frac{7}{30} m^{9} n^{7} \)

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: \[ \frac{7}{30} m^{2} n^{7} \]