Expressions with Exponents

What do you notice? What do you wonder?

You find a brass bottle that looks really old. When you rub some dirt off of the bottle, a genie appears! The genie offers you a reward.

You must choose one:

$50,000,

or

A magical $1 coin. The coin will turn into two coins on the first day. The two coins will turn into four coins on the second day. The four coins will double to 8 coins on the third day. The genie explains the doubling will continue for 28 days.

• $50,000

• A magical $1 coin

Money Problem:

The number of coins on the third day will be 2⋅2⋅2. Write an equivalent expression using exponents.

• $2^2$

• $2\cdot3$

• $2^3$

Tags

CCSS.6.EE.A.1

What do  $2^5$ and $2^6$ represent in this situation? Evaluate  $2^5$ and $2^6$  without a calculator.

Tags

CCSS.6.EE.A.1

Money Problem:

How many days would it take for the number of magical coins to exceed $50,000?

• 12

• 13

• 14

• 15

• 16

Tags

CCSS.HSF.LE.A.4

Money Problem:

Will the value of the magical coins exceed a million dollars within the 28 days? Explain or show your reasoning.

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.

• $2^3\cdot2$

• $4^2$

• $\frac{2^5}{2}$

• $8^2$

Tags

CCSS.6.EE.A.1

Write three expressions containing exponents so that each expression equals 81.

Tags

CCSS.6.EE.A.1

Find the values of  $3^x$  and  $\left(\frac{1}{3}\right)^x$  for different values of x. What patterns do you notice?

Tags

CCSS.HSF-IF.C.8B

True or False?

 $2^4=2\cdot4$  

• True

• False

Tags

CCSS.6.EE.A.1