Whole number exponents with integer bases 2

Whole number exponents with integer bases 2
Description
Exercise Name:	Whole number exponents with integer bases 2
Math Missions:	Pre-algebra Math Mission, Algebra basics Math Mission, Mathematics I Math Mission, Algebra I Math Mission, Mathematics II Math Mission
Types of Problems:	1

The Whole number exponents with integer bases 2 exercise appears under the Pre-algebra Math Mission, Algebra basics Math Mission, Mathematics I Math Mission, Algebra I Math Mission and Mathematics II Math Mission. This exercise starts expanding the positive exponents to larger exponents that can be interpreted quickly.

Types of Problems

There is one type of problem in this exercise:

1. Find the value of the expression: This problem asks the student to correct evaluate an numerical exponential expression and write the answer in the space provided.

   

   Find the value of the expression

Strategies

To complete this exercise all that is required is knowledge of the definition of the exponent, but it would be time-consuming by the definition in some cases.

1. The definition of the exponent is repeated multiplication. In other words, ${a^b}$ is ${a}$ being multiplied by itself ${b}$ many times.
2. One raised to any power is one.
3. Zero raised to any positive power is zero.
4. Negative one raised to a power is one is the exponent is even, negative one if it is odd.
5. In general, numbers raised to even powers will always be positive, while if a number is raised to odd powers it will retain it's initial sign.

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).
2. Exponents are used in Computer Game Physics, pH and Richter Measuring Scales, Science, Engineering, Economics, Accounting, Finance, and many other disciplines.
3. Exponential Growth is a critically important aspect of Finance, Demographics, Biology, Economics, Resources, Electronics and many other areas.
4. Exponential Decay is associated with Light, Sound, Sporting Fixtures, Dangerous Chemicals, and Radioactive Waste.
5. People who use Exponents are Economists, Bankers, Financial Advisors, Insurance Risk Assessors, Biologists, Engineers, Computer Programmers, Chemists, Physicists, Geographers, Sound Engineers, Statisticians, Mathematicians, Geologists and many other professions.