The colonists stated that they were now free and independent states. what did this statement make then think they had the power to do

As free and independent states, the American patriots believed they had the authority to withdraw from British colonial control.  They also believed that they had power to do all the things that free and independent states can do -- make alliances, establish trade with other countries, go to war and make peace with other nations, etc.

In the Declaration of Independence (1776), "the thirteen United States of America" unanimously declared "that these united Colonies are, and of Right ought to be Free and Independent States, that they are Absolved from all Allegiance to the British Crown, and that all political connection between them and the State of Great Britain, is and ought to be totally dissolved; and that as Free and Independent States, they have full Power to levy War, conclude Peace, contract Alliances, establish Commerce, and to do all other Acts and Things which Independent States may of right do."

This strong statement was made toward the end of the Declaration of Independence.  In the section preceding that, Thomas Jefferson (lead author of the Declaration) had presented a list of "facts to be submitted to a candid world," which demonstrated that the British king had been seeking to establish "an absolute Tyranny over these States." In the eyes of the American revolutionaries, their assertion of independence was justified because the British government had habitually acted in tyrannical ways toward the colonies.  The principle of the social contract gave the colonists the right to terminate their ties to British government and establish their own government which would be better suited toward protecting their natural rights.

For more on the idea of the social contract, Read more on

the manhattan project's indispensable man

the correct answer is: (1) affected by gerrymandering; (2) not affected by gerrymandering.

gerrymandering is known as a practice that intends to establish a some kind of political advantage for a particular party or group. to do this district boundaries are manipulated. the new resulting district is named a gerrymandering.

in other words, what gerrymandering does is to draw the boundaries of electoral districts trying to benefit the party who is doing it. sometimes, the party controlling the legislature will redraw it so they can maximize the number of districts they are likely to control.