The Last Digit
What is the last digit of 4^{5456468}? Explain your reasoning.
What is the last digit of 3^{897}? Explain your reasoning.

Extensions 
Investigate patterns in the digits of the exponentiation of other integer bases.

Related External Resources 
Digits, squares, and cycles
Explore fascinating patterns that lurk among the digits of whole numbers.
Mayan adventure [ java applet ]
This is a multipage javabased Mayan Adventure game. Explore Mayan Mathematics, the Mayan system of time keeping, and significant facts about Mayan culture & history, while deciphering up to 40% of all extant Mayan hieroglyphics.
Sequence of exercise
Two students decided to begin a new exercise program they agreed that they would jog 3 blocks farther each day. Determine how many days the students have been jogging.
Blanketyfive squared
BlanketyFive Squared is a fun game that will teach you to square twodigit numbers that end in five.
Assorted problems
Assorted problems of the day from Highland Middle School.
Submit your idea for an investigation to InterMath.
