Matching



Angelina used a pattern to solve a problem with powers. She noted that the last 2
digits follow the pattern. Order the steps Angelina used to predict the last 2 digits of
7^{22}.
A.  She made a pattern using base 7 and
exponents.  B.  She checked her work to see that she did it
correctly.  C.  She determined that 7^{22 }would be in the second
column.  D.  She calculated that all numbers in the second column had 49 as
the last two digits.   


1.

What
is Angelina’s first step?


2.

What
is her second step?


3.

What
is her third step?


4.

What
is her final step?

Numeric Response


5.

What
are the last 2 digits for 7^{15}?


6.

What
are the last 2 digits for 7^{28}?


7.

What
are the last 2 digits for 7^{100}?


8.

What
are the last 2 digits for 7^{101}?



Determine the last digit of each power by using a strategy
like Angelina’s.


9.

4^{44}


10.

6^{52}
