An exponent is way of written math in shorthand. In a way, it is abbreviated math. It is a way of telling us how many times a number is multiplied by itself. The exponent is written in a superscript which mean in a smaller size to the upper right corner of the base number. The root number (the larger number to the left) is the number that will be multiplied by itself. 74 is an example. The root number is 7 and the exponent is 4. This indicates that 7 will be multiped by itself 4 times. This means that 74 = 7 x 7 x 7 x 7. You may here this also refer to as being “raised to a power of”. Anything that is raised to the) power is equal to a value of 1. Using exponents saves us from writing things in out in a tedious fashion. Operations between values that share this form shorthand a sped up greatly. As you begin to work with very large values, they come in quite handy.
- Comparing Exponents - I like to have students estimate their answers prior to comparing the final values.
- Exponential Decay - Students will learn to under how items break down over time.
- Evaluating Negative Exponents - Students learn how to work at the fundamental level and then advance to including operations.
- Evaluating Numerical Expressions with Exponents - In this section you will use all the rules you have learned in this topic.
- Fractions with Exponents - This is often difficult when students first encounter this skill.
- Naming and Introducing Exponents - You will learn how to verbalize what is set in an expression.
- Powers of Ten and Scientific Notation - Students will start to understand the power of understanding exponents.
- Products and Quotients to a Power - We learn two new rules to apply to equations and equations.
- Products of Exponents (Product Rule) - As long as the bases are the same, you just add the exponents together.
- Properties of Exponents and Roots - How to quickly learn to simplify values that are presented to you.
- Properties of Exponents - High School Expression Based : This is for the high-level equations.
- Properties of Integer Exponents - This teaches you how to approach complex equations.
- Quotients of Exponents - This is the inverse of the Product Rule. If the bases are the same, we subtract the exponents.
- Rational Exponents - Students learn to become more comfortable with complex expressions.
- Rewriting Radical and Exponential Expressions - This is almost always the first step to approaching these expressions.
- Scientific Notation - This form of writing values is rooted in this skill to make large and small values easier to work with.
- Solving Common Base Exponential Equations - This is when you are pondering so serious algebra.
- Solving Exponential Equations (Lacking a Common Base) - You will start to use the log rule to simplify what you are working with.
- Square and Cube Roots - We learn how to quickly go after these types of problems.
- Square Root Word Problems - These problems were difficult to write.
- Zero and Negative Exponents - You will truly master these skills with these worksheets.
Tips for Teaching Exponents
Exponents are the shortcut version for expressing the multiplication of a number by itself. In other words, the number of times a number is multiplied with itself determines the concept of exponents. If you are teaching exponents to your students, highlighted tips can help your case extensively.
First, teach them the concept of powers so that they know what the exponents are all about. It's better to choose an example of 2.
Additionally, there are a few definite rules which you must teach your student. Such that any number raised to the power of 0 will always be equal to 1. Moreover, any number having a power 1 will be similar to the number itself.
There are a few properties that you must teach your students next. These properties are as follows.
If you multiply two terms which has the same base, then the powers will be added, i.e. x3 × x4 = x(3+4) = x7
If you divide two terms that have the same base, then the powers are subtracted such that the one on the denominator gets subtracted from the one in the numerator. Such that x3 ÷ x4 = x (3-4) = x(-1)
If you have an exponent expression which has power outside as well. Then the powers get multiplied. For example, (am)n = a(m×n) = amn
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How This Skill Is Used in the Real World
You will commonly come across words that related directly to this concept. You will commonly see the words indexes, powers, or indices used in fields that are attempting to gauge growth or losses. Most technology fields lend themselves clearly to these measures. Computer game manufacturers use these measures to move things around your screen and change the perception of how big things are on it. Scientists use this measure to understand the amount of a substance that exists in front of them. Economists gauge how the financial world is trending and as to whether we are living in a time of prosperity for citizens using this concept in a more complex environment. Sound engineers learn how to arrange a sound setup for the best acoustic experience for an audience using this skill to determine how sound waves can best be managed in a given surrounding area. Marketers learn the potential of a viral communication through analyzing the potential growth of that communication across platforms with this basic concept. Investors can calculate the potential of a moderate investment by using the fundamentals of compounding which is rooted in this skill. As you can see, in just the few instances we looked at here, this skill has way too many applications in our daily lives to list. Take a look at all the worksheet topics above to begin to explore the potential of this concept in your life.