A figure of a series of dot branches. In the center is a black dot. Three branches extend from the black dot with one red dot at the end of each branch. There are three branches that extend from each red dot with one green dot at the end of each branch. There are three branches that extend from each green dot with one yellow dot at the end of each branch. There are three branches that extend from each yellow dot with one blue dot at the end of each branch.
12.2
Activity
12.3
Activity
Here are some expressions. All but one of them equals 16. Find the one that is not equal to 16 and explain how you know.
Write three expressions with exponents so that each expression equals 81.
Student Lesson Summary
When we write an expression like , we call the exponent.
If is a whole number, it tells how many factors of 2 we should multiply to find the value of the expression. For example, , and .
There are different ways to say . We can say “two raised to the power of five” or “two to the fifth power” or just “two to the fifth.”
None
A wealthy king wanted to reward the inventor of chess for creating a beautiful game. The king offered the inventor a chest of jewels, a palace, or land to rule.
The inventor declined these rewards and said that all he wished for were some grains of rice.
Shocked, the king demanded an explanation.
The inventor explained, “On the first day, give me 2 grains of rice for the first square on the chessboard. On the second day, give me 4 grains of rice for the second square on the board, and 8 on the third day. Keep doubling the grains of rice each day for each of the 64 squares on the board.”
The king and all the members of his court burst out into laughter. “How foolish! You decline the treasures I offer for a few handfuls of rice?”
Do you think the inventor was foolish?
Complete this table to show the number of grains on the first 5 days.
day
expression with repeated multiplication
expression with exponents
number of grains of rice
1
2
2
4
3
8
4
5
What does represent in this situation? Find the value of without a calculator.
Pause for discussion.
How many days would it take for the number of grains of rice to exceed 50,000?
Will the number of grains of rice exceed 1 million before half of the chessboard is reached? Explain or show your reasoning.
