if the number in scientific notation is between 1 and 10, is dividing the product of coefficients by 10 and raising the power of 10 by 1 still necessary?

No, if the number in scientific notation is between 1 and 10, dividing the product of coefficients by 10 and raising the power of 10 by 1 is not necessary. This is because a number between 1 and 10 already has a coefficient between 1 and 10, so there is no need to divide by 10 and increase the power of 10.