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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.
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.

## 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 (${0.000000001}$).