Are you having trouble learning exponential forms and want to learn more about them? You have come to the right place! In this post, we will tell you everything you need to know about exponential form, including how to write, simplify, and determine it. Just read on, and you will feel like having a lesson from a professional tutor!
What is Exponential Form?
The concept of the exponential form may sound confusing, but it is effortless instead. It is simply a shortcut to writing numbers that are being multiplied by themselves more than one time. The exponential form contains base and exponents, and it helps in simplifying an equation.
Example of Exponential Form:
If an equation is 6 x 6 x 6 x 6, then its exponential form will be:
In this, 6 will be the base, and 4 will be the power. Power will determine or identify how many times the base number is being multiplied.
How to Write in Exponential Form?
We can convert almost all the Mathematics expressions into Exponential form to cover the repeated multiplication. The most typical expression of exponential form will look like this:
- 5 x 5 = 52
- 8 x 8 x 8 = 83
- 3 x 3 x 3 x3 x3 = 35
Now, if we want to reverse these expressions, they will be like these:
- 25 = 5 x 5 = 52
- 512 = 8 x 8 x 8 = 83
- 243 = 3 x 3 x 3 x 3 x3 = 35
This reversing situation is used to factor out the numbers in numerical problems.
You can also use exponential equations and exponents to simplify and rewrite large numbers. This process is called the Standard Exponential Form.
For example, we have a number 534,000; we are going to simplify it like this:
- 5.34 x 10,000 = 5.34 x 104
This exponential form mentioned above is known as scientific notation. To find the power of a large number, all you need to do is count the zeroes. 10,000 had four zeroes in it so that the power would be 104.
To help you have a better understanding, here is a detailed table of the three forms used to represent numbers:
|Standard Form||Factor Form||Exponential Form|
|6||1 x 6||61|
|100||2 x 2 x 5 x 5||22 x 52|
|256||2 x 2 x 2 x 2 x 2 x 2 x 2 x 2||28|
How to Convert Exponential form to Logarithmic Form?
You can even convert the exponential form into logarithmic form with a straightforward and easy-peasy procedure. The logarithmic formula is:
- If ea = b, then logeb = a.
Here is an example:
If we have an exponential form of 62 = 100, here, b = 100, a = 2, and e = 6. The logarithmic form of this equation will be:
log6100 = 2.
How to Convert Exponential Form to Radical Form?
To convert an exponential form into a radical form, we use the formula:
- xm/n = n√xm
The √ symbol is radical, and it represents the nth roots. To do the conversion, we have to shift the denominator of the exponent to the left side of the radical. Also, the numerator will change into the power of the radical.
For example, if we have an exponential form of 93/4, then its radical form would be 4√93.
To better understand the concept of Exponential Forms and how to solve its questions, here is a detailed video explanation:
I hope we made the concept of the Exponential Form clear for you. However, if you still have any doubts or confusion, please contact us and request a professional Mathematics Tutor for more clarification.