Multiplying Exponents Made Easy!

Rules Of Exponents Worksheet - Multiplying Exponents Made Easy!

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Multiplying Exponents Made Easy!

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Rules Of Exponents Worksheet

Exponents are repeated multiplication of a whole by itself. For example; if we want to multiply 2 by itself, then it can be written by the following two ways:

2 * 2, which is the general way to show multiplication or 2² is the exponential way to show 2 times 2.

In other words 2 * 2 = 2²

Similarly 2 * 2 * 2 = 2³ is the exponential form when two is multiplied by itself three times.

Remember, 2² is read as 2 to the power 2 and similarly 2³ is read as 2 to the power 3.

Also in the exponential term, 2³; 2 is called base and 3 is the exponent.

So far we have explored the basic exponents. Let's go further to examine the rule to multiply two exponents, which means how to multiply two exponents.

To multiply two or more exponents care should be taken about the base of the exponents. Depending upon the kind of the bases of the terms there are two ways to multiply the exponents.

1. Multiplying exponents with different bases:

To multiply two or more exponents with different bases, we have to solve the exponents individually and then multiply the answers with each other. For example; reconsider we want to multiply 2² and 3²; both terms have different bases 2 and 3 respectively and have same power 2. As both the terms have the different bases, they will be multiply as follows: 2² * 3² = 4 * 9 = 36

So, we solved 2² as 2 * 2 to get 4 and 3² as 3 * 3 to get 9 and multiplied the 4 and 9 to get our final acknowledge 36.

Hence to multiply exponents with the different bases, solve the exponents first and then multiply the answers to find the final solution for the problem.

2. Multiplying the exponents with same bases:

To multiply the exponents with the same bases, the powers are added to get the one term and then the terms are expanded to solve and get the answer. For example; reconsider we want to multiply 3² and3³; both the terms have the same base which is three but different powers which are 2 and 3. The multiplication will be carried out as shown below:

3² * 3³ = 3^5 [3^5 is read as 3 to the power 5]

And 3^5 = 243

Hence to solve 3² * 3³; we added the powers 2 + 3 to get the new power 5 and kept the base same as tasteless base 3. Then we solved the 3^5 by expanding it as 3*3*3*3*3 = 243.

Note that we add the exponents only if the bases are same and getting multiplied with each other.

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