Last Updated on October 4, 2023 by Editorial Team
Have you ever encountered a number given as the superscript of another number? At first, it can be bewildering for the students to comprehend what exactly it is and what it signifies. Well, the concept of exponents is what is being employed in this case.
When there is a situation where one needs to present a large number, it is compacted and written in the form of exponents making it easier to write and remember. In many countries, exponents are called indices, but the good news is that the concept is the same no matter what term is used.
Nevertheless, introducing exponents can be dreading because the students fall into the rookie pattern of multiplying the base with the exponent. Fortunately, we can apply certain criteria to simplify those equations for a more readable appearance and more straightforward calculation.
But, while talking about exponents, it’s not just that they are difficult to follow, but we feel that it is just another subject kids feel whose relevance stays just inside the classroom. However, did you know that concepts like exponents and powers are used more in fields such as finance and science than in any other? Here is a quick preview of how it influences multiple professions and how you use it in daily life.
Exponents: A tough nut to crack?
“New” numbers in the extension of a number system often have rules and definitions that differ from previously recognized numbers. Natural numbers, for example, are most familiar to kids in their early years of school. The addition of zero, on the other hand, expands the number system from natural numbers to whole numbers and forces students to adapt or update the preceding concepts and representations in their brains, which they cannot always do.
Sixth-grade kids, for example, have trouble determining whether zero is an even number. In this regard, the process of expanding the number system is difficult for both teachers and students. Although most students think of exponents as separate number sets, they allow them to shorten repeated multiplications of the same number.
Exponents are difficult to grasp because they demand consideration of the relationship between symbols, meanings, and the algorithmic features of exponentiation. In this process, procedural knowledge is insufficient to do the necessary calculations to determine the value of exponential expressions without comprehending the reasoning behind algorithms and the number system hierarchy.
For example, when calculating the numerical value of an exponential equation, students frequently multiply the base by the exponent. Exponentiation, on the other hand, incorporates laws concerning base and power. This arrangement causes problems since the kids become confused and fail to recall the regulations. In support of this notion, studies[1] have demonstrated that students see exponents as hard and challenging concepts that are disconnected from ordinary life.
Uses of exponents in real life
In the previous section, we mentioned that kids don’t find hard math concepts such as exponents worth their while primarily because they think it won’t help them anywhere in real life. However, to break that myth we are here to help kids see the use of exponents in day-to-day life.
1. Scientific Scales
Any time a scientific field uses a scale, like the pH scale or the Richter scale, you can bet you will find exponents. This is because the pH scale and the Richter scale are logarithmic relationships, with each whole number representing a ten-fold increase from the number before. Not just that even in chemistry exponents are widely used to calculate the mass of protons, electrons, etc.
For example, when chemists indicate a substance has a pH of 7, they know this represents 10⁷, while a substance with a pH of 8 represents 10⁸. This means that the substance with a pH of 8 is 10 times more basic than the substance with a pH of 7.
2. Taking Measurements
Taking measurements and calculating multi-dimensional quantities can be another real-world application of exponents. Because the area is a two-dimensional measure of space (length x breadth), it is usually measured in square units such as square feet or square meters. When calculating the area of a garden bed in feet, for example, you should supply the solution in square feet or ft2 using an exponent.
Similarly, volume is a three-dimensional measure of space (length x breadth x height); hence it is always measured in cubic units such as cubic feet or cubic meters. So, for example, if you wanted to compute the volume of a greenhouse, you would use an exponent to provide the answer in cubic feet or ft3.
Science fields such as biology and physics work with such small distances, that additional units are required. A micrometer is 1×10⁻⁶ of a meter. It is often used in biology to quantify bacteria and infrared radiation wavelengths. It is also known as a micron and is denoted by the symbol. There are also nanometers (1×10⁻⁹ of a meter), picometers (1×10⁻¹² of a meter), femtometers (1×10⁻¹⁵ of a meter), and attometers (1×10⁻¹⁸ of a meter).
3. Computer
Another valid use of exponents is while speaking about computers. For example, there are multiple significant digits if we talk about the computer’s memory. However, with the help of exponents, you can easily describe the computer’s memory.
Other uses of exponents in computers are data entry, programming, calculation programs, and much more. Can you imagine a programming application without exponents? Indeed, the usage is undeniable. The prime example of exponents in computers is while measuring memory e.g. 1GB=10⁹ bytes.
4. Earthquake Intensity
The Richter scale, for years, was used to describe the energy released by earthquakes. Currently, the most common way to measure the same is the Moment Magnitude Scale, which follows the same mathematical course. Hereby, to record the amplitude of the vibration caused is in mm as ten raised to an exponent, then add 3 to the exponent, x. For example, if the amplitude is 100mm, rewrite it as 10². Adding 3 to the exponent gives Richard scale a rating of 2+3=5.
5. Finance: Compound Interest
Compound interest is calculated with the help of exponential functions. A specific sum is added to the account balance each time money is invested (or lent out). Interest is the amount of money that is added to the balance. The sum will continue to accrue interest after that interest has been added during the subsequent compounding period.
Formula for compound interest: A = P(1 + r/n)nt
Where, A = amount || P = principal || r = rate of interest || n = number of times interest is compounded per year || t = time (in years)
Compound interest refers to the concept of earning interest on interest. There are numerous ways to pay interest. The first method, as previously mentioned, is compounded yearly. The interest is paid once a year according to this plan. However, interest can compound more frequently. Compounding semi-annually (twice a year), quarterly (four times a year), monthly (12 times a year), weekly (52 times a year), or even daily is a widespread practice (365 times per year).
Tips to simplify exponents
Exponents are a difficult concept; thus, teaching it in old traditional ways can confuse the kids. Therefore, check below some creative ways to simplify exponents and make them easy and fun to learn.
1. Introduce learning activities
Learning a concept while performing activities can be an ideal way to teach kids the concept of exponents. You can engage them in a little folding origami game or deck up the cards to allow them to learn how to power up a number in a rather funny manner. If you are looking for some fun activities to teach kids exponents, check here.
2. Take help from online games.
Exponents are tricky, but playing games to lean exponents can provide plenty of practice! Teachers frequently struggle to explain to the students the differences between, say, A times n and A to the power n. (the difference between multiplying by n and raising exponentially to the power n). Math beginners can learn to understand and apply the concept of exponent confidently and fluently with learning tools like online games.
3. Let them know the relevance of the entire concept
When you have a picky learner, you need to make them understand what the concept means and it will affect them in the future. Allow them to figure out its essence using multiple examples. Check the real-life application discussed above if you are having difficulty picturing real-time examples.
Summing up
Students frequently wonder if they will ever need to use their math skills in real life. They presumably grasp the importance of elementary arithmetic concepts like addition and multiplication, but by middle school, some kids may be wondering why they should even learn subjects like square roots or integers.
However, Exponents are not just a mathematical concept that kids need to learn to pass a test. As you might have seen in most fields, be it science, mathematics, or finance, exponents are widely used. Thus, incorporate fun activities and make them understand the subject’s relevance before applying the theoretical approach.
Reference
- Iymen, Esra & Duatepe-Paksu, Asuman. (2015). Analysis of 8th Grade Students’ Number Sense Related to the Exponents in Terms of Number Sense Components. TED EĞİTİM VE BİLİM. 40. 10.15390/EB.2015.2710.
An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,