Addition has always been sweet, even multiplication was cool. But are you in mood of new operations that grows numbers at a faster rate than addition or multiplication? Want to explain how majority things in this universe grow and shrink. You have your answer and that operation is known as exponents.

Let’s understand what exponents are:

To understand exponents in greater depth, let us start it with a game. Grab a normal piece of paper and start folding it in half. Scientifically, it’s said that you can fold a paper in half, a maximum of eight times and not more than that. But in end, you will notice that the paper after folding it for seven to eight times that you’re holding in your hand is considerably much thicker than the piece of paper you initially took.

Now, take a paper which can hypothetically be folded about 50 times. How much do you its thickness will be? 5 inches? 12 inches? Keep guessing, but even your most ambitious guesses won’t be right. The correct answer to this question is the distance between the sun and the earth. Amazed? Should be.

Let’s understand how.

The thickness of any usual bit of paper is around \(\frac{1}{200th}\) of an inch. Hence, every time if you fold that paper, you will be doubling its thickness. So, initially you will be having the original thickness of the paper multiplied times 2, times 2, times 2, …….etc. So eventually you have multiplied the original thickness of the paper \(2^{50}\) times. The number \(2^{50}\)is extraordinarily an enormous number that even if it is multiplied by a number as small as \(\frac{1}{200}\), it won’t make a huge difference.

In this game, the value \(\frac{1}{200}\) is the exponent value, where 2 is base and 50 is the exponent. The exponent is used for representing the number of times the base value is multiplied with itself. Both the base and exponent can be any real number; it is not only confined to positive integers.

## Properties of Rules of Exponents

- An even exponent will always yield positive values.
- Zero raised to any power will always yield zero.
- 1 raised to any power will yield 1.
- -1 raised to even power yields 1, otherwise it’s -1.
- When a proper fraction is raised to any power, the resultant is less than the actual number.
- When a fraction is raised to a power, the exponent value contributes to both, numerator and the denominator.
- Multiplying exponents with same base: If the base is same then simply add the exponents.
- Dividing exponents with same base: Simply subtract the exponents and keep the base same.
- When you are raising an exponential power to a power then to get the final value multiply the exponents.
- When multiplying exponents with different bases but same exponents, then keep the exponent same and multiply the bases together.
- When dividing exponents with different bases but same exponents, then keep the exponent same and divide the bases.
- For negative exponents, flip the base. That is, if it is in numerator make it in denominator or vice versa.
- These are some of the properties that can help you solve exponents with extreme ease.

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