Explain how delegated powers, reserved powers, concurrent powers and denied powers share and divide power among national, state, and local goverment.

Delegated powers are those powers specifically granted to the federal government by the United States Constitution.

Reserved powers are powers not specifically granted to the federal government, and thus reserved for the states.

Concurrent powers are powers where both the federal and state government will have involvement.

Denied powers refer to powers specifically denied to one or another level of government within the Constitution.

Some examples:

Delegated powers include such things as the power to coin/print money, the power to establish and impose tariffs, and the power to regulated trade with foreign nations and trade/commerce between states.

Reserved powers include such things as educational systems (schools) and curriculum taught, regulation of industry and trade within a state, and punishments for crimes under state law.  (Note, for instance, that some states have a death penalty for those convicted of murder, and other states do not have a death penalty.)  

Concurrent powers include things that both the federal government and state governments do in their own respective domains.  One examples would be establishing courts and prison systems (for state cases and federal cases).  Another example would be taxation -- both the federal government and state governments have authority to assess taxes.  Another would be holding elections -- national elections under federal supervision, other elections on the state level under state supervision.

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