Whole number exponents with integer bases

Whole number exponents with integer bases
Description
Exercise Name:	Whole number exponents with integer bases
Math Missions:	7th grade (U.S.) Math Mission, 8th grade (U.S.) Math Mission, Pre-algebra Math Mission, Mathematics I Math Mission
Types of Problems:	2

The Whole number exponents with integer bases exercise appears under the 7th grade (U.S.) Math Mission, 8th grade (U.S.) Math Mission, Pre-algebra Math Mission and Mathematics I Math Mission. This exercise continues practice with interpretation of exponents, now expanding to integers as bases.

Types of Problems

There are two types of problems in this exercise:

1. Find the value: This problem has a numerical exponential expression and asks the user to find the correct answer and write it in the space provided.

   

   Find the value

2. Select correct interpretation: This problem gives either a repeated multiplication expression or an exponential expression. The user is asked to convert to the other form and select the corresponding answer from the multiple choice list.

   

   Select correct interpretation

Strategies

To complete this exercise the main thing to keep in mind is that exponents are an abbreviation for repeated multiplication.

1. The expression ${a^b}$ can be interpreted as a being multiplied by itself b many times.
2. When entering answers in a text box, pressing enter on the keyboard will submit the answer more quickly than clicking a mouse button.
3. The Select correct interpretation problem requires a correct expression, not an expression that is equivalent to. For example, ${1\times 1\times 1=1^3=1^2}$, however, ${1^3}$ is the "correct interpretation" although ${1^2}$ evaluates to the same value.

Real-life Applications

1. An kind of indirect example of using exponents is when one talks about extremely tiny or extremely big quantities. For example, the term "nanometer" means ${10^{-9}}$ meter. The prefix "nano" means the number ${10^{-9}}$, which is an extremely small decimal number (${0.000000001}$).