IM 8.7.1 Lesson: Exponent Review

Which expression does not belong? Explain how you know.
[table][tr][td][math]2^3[/math][/td][td][/td][td][math]3^2[/math][/td][/tr][tr][td][/td][td][/td][td][/td][/tr][tr][td][math]8[/math][/td][td][/td][td][math]2^2\cdot2^1[/math][/td][/tr][/table]
Mai and Andre found an old, brass bottle that contained a magical genie. They freed the genie, and it offered them each a magical $1 coin as thanks.
[size=150][list][*]The magic coin turned into 2 coins on the first day.[/*][*]The 2 coins turned into 4 coins on the second day.[/*][*]The 4 coins turned into 8 coins, on the third day.[/*][/list]This doubling pattern continued for 28 days.[/size]
[size=150]Mai was trying to calculate how many coins she would have and remembered that instead of writing [math]1\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2[/math] for the number of coins on the 6th day, she could write [math]2^6[/math].[/size][br][br]The number of coins Mai had on the 28th day is very, very large. Write an expression to represent this number without computing its value.
Click on the arrow to see the coins start to magically multiply.
Andre’s coins lost their magic on the 25th day, so Mai has a lot more coins than he does. How many times more coins does Mai have than Andre?
After a while, Jada picks up a coin that seems different than the others. She notices that the next day, only half of the coin is left!
[size=150][list][*]On the second day, only [math]\frac{1}{4}[/math] of the coin is left.[/*][*]On the third day, [math]\frac{1}{8}[/math] of the coin remains.[/*][/list][/size][br]What fraction of the coin remains after 6 days?
What fraction of the coin remains after 28 days? Write an expression to describe this without computing its value.
Watch the magical coin changing for ten days with this applet.
Does the coin disappear completely? If so, after how many days?
Every animal has two parents. Each of its parents also has two parents. Draw a family tree showing an animal, its parents, its grandparents, and its great-grandparents.
[size=150][size=100]We say that the animal’s eight great-grandparents are “three generations back” from the animal. [/size][/size]At which generation back would an animal have 262,144 ancestors?

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