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Exponential Rules

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Exponential Rules

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!

What are the exponential rules?

Here is the full list of exponential rules.

1. Multiplication:

Add the powers

2. Division:

Subtract the powers

3. Power to a Power:

Multiply the powers

4. Powers of 0:

5. Negative Powers:

Take the reciprocal

6. Fractional Powers:

Take the root

How do you use the exponential rules?

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:

1. Multiplication

cannot be simplified further because the bases are different

2. Division

3. Power to a Power

4. Powers of 0

5. Negative Powers

6. Fractional Powers

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!

Exponential Rules - Key takeaways

  • The exponential rules/index laws are important rules to follow when doing calculations involving exponents.

Frequently Asked Questions about Exponential Rules

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

Final Exponential Rules Quiz

Question

What is the multiplication law?

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Answer

Add the powers.

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Question

What is the division law?

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Answer

Divide the powers.

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Question

How do you calculate a power to a power?


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Answer

Multiply the powers.

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Question

How do you calculate a power of 0?


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Answer

Any number to the power of 0 is equal to 1.

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Question

What does a negative power do?


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Answer

It takes the reciprocal of a number.

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