Exponents & Its Properties: Math

A common subject area seen in the math section of most exams is exponents. You are very likely to encounter these in the exam. Moreover, these problems can pose a challenge for many test takers. By paying a little attention, you can easily solve problems from this area.

Exponents represent the times any number should be multiplied with itself. For instance, 4x4x4 can be written as 43. In this case, the number 3 is the exponent while 4 is the base. Obviously, base is the number which is being multiplied and exponent tells you the number of times you should multiply the number. Exponent are also often referred to as power and the process of using them is called raising to a power.

So, 43 can be stated as four raised to the third power. You would have heard of terms ‘squared’ and ‘cubed’. When the exponent is 2, a number is squared i.e is multiplied by itself. For instance 22 means 2×2=4. While it may seem a more complicated way of representing numbers, it is extremely useful when dealing with variables.

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There are negative exponents as well and you do just the opposite with them – divide. A negative exponent indicates the number of times you have to divide 1 by that number. For example, 5-1 means 1/5 which is 0.2.

Before you delve deeper, you need to understand one basic rule. Anything raise to the power of 0 is 1. So, x0 will always be equal to one. This rule can come in handy while solving exponent problems.

Apart from that, there are some other rules:

Whenever you multiply two terms with the same base, you can add the exponents. For instance, (23) (22) can be written as 25.

If an exponent expression itself is raised to a certain power, you can multiply the exponent and power. For instance, (23)2 can be represented as 26.

However, do not follow this rule if there is an addition or subtraction action within the brackets. For instance, (2+3)3 does not mean 23+33=35. It actually means (53) for which the answer is 125. A lot of mistakes can happen when tackling such questions, especially when variables are involved.

Remember this tip – When in doubt, always break down the expression!

Watch a video on Exponent Properties.

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