Zero at Work

In 7x^0, the exponent 0 applies only to the x. For nonzero x, x^0 = 1, so 7x^0 = 7 * 1 = 7.

With parentheses, the whole product is the base. For nonzero x, (7x)^0 = 1, because the exponent now applies to 7x as a whole. The example shows that the parentheses decide what the exponent applies to.

A zero exponent turns its base into the factor 1. The rest of the expression stays as it is. So 7x^0 keeps the 7 and loses only the x.