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The exponential rules are laws you must follow when doing calculations involving exponents. These are very important to remember, so make sure you practice them all until you feel confident!
Here is the full list of exponential rules.
Add the powers
Subtract the powers
Multiply the powers
Take the reciprocal
Take the root
You use the exponential rules by breaking down each part of the power and identifying which rule is applicable - for example, looking for fractions and signs. For the first two rules, it’s important to remember that you can only simplify expressions if the same number is being raised to different powers.
Here are some examples of each rule to help you to understand how they work in practice, including some more complex cases:
cannot be simplified further because the bases are different
Note: You can simplify this in any order, so the following would also work:
For obvious reasons, it’s often best to choose the simplest order!
The exponential rules are laws you need to follow when doing calculations which involve powers. An example is that when you multiply two of the same number raised to an exponent, you add the exponents together. See the article above for the full list!
There are six laws of indices which are important to remember, although the laws for multiplication, division and brackets are considered the main ones.
The three main laws of indices, also known as exponential rules, relate to multiplication, division and brackets. They are as follows:
x^a ⋅ x^b = x^a+b
x^a / x^b = x^a-b
(x^a)^b = x^a⋅b
What is the multiplication law?
Add the powers.
What is the division law?
Divide the powers.
How do you calculate a power to a power?
Multiply the powers.
How do you calculate a power of 0?
Any number to the power of 0 is equal to 1.
What does a negative power do?
It takes the reciprocal of a number.
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