Express the product of \( 3.2 \times 10^{6} \) and \( 4.1 \times 10^{-1} \) in the standard form. \( \begin{array}{ll}\text { (a) } 1.312 \times 10^{5} & \text { (b) } 1.232 \times 10^{6} \\ \text { (c) } 1.312 \times 10^{6} & \text { (d) } 1.312 \times 10^{7}\end{array} \)

To find the product of \( 3.2 \times 10^{6} \) and \( 4.1 \times 10^{-1} \), we first multiply the coefficients (the numbers in front): \[ 3.2 \times 4.1 = 13.12. \] Next, we handle the powers of ten. When multiplying, we add the exponents: \[ 10^{6} \times 10^{-1} = 10^{6 + (-1)} = 10^{5}. \] Now, we combine these results: \[ 13.12 \times 10^{5}. \] To express this in standard form, we need a coefficient between 1 and 10. Therefore, we rewrite 13.12 as: \[ 1.312 \times 10^{1} \] Now, we can combine the powers of ten: \[ 1.312 \times 10^{1} \times 10^{5} = 1.312 \times 10^{(1 + 5)} = 1.312 \times 10^{6}. \] So, the final answer in standard form is \( 1.312 \times 10^{6} \). Thus, the answer is \( \text{(c) } 1.312 \times 10^{6} \).