Understand the product rule for exponents

Practically, the rule is very simple and easy to understand, but it pay attention and try to make a reflex of knowing when to use this rule. The rule must be practiced in a series of simple but very useful exercises. Before laying down the actual product rule for exponents, we must make sure you are aware of another simple and basic algebra rules. An algebra important basic rule is that: any nonzero number raised to 0 equals 1.

  • There are two "rules of 1" you must always keep in mind. First of them says that any number raised at the power 1 equals itself. The rules is totally logical because the power shows how many times a number is multiplied by itself. Being multiplied only once, the result will be the number itself.

  • The second rule is even more logical. It says that one raised to any power is one. I don't believe you will have problems in understanding that, so we will move forward.

Now that you have this basic rules clear in your mine, is time to offer you the enunciation for the product rule of exponents: when you multiply two powers which have the same base, you can add the exponents and let the base unchanged. The rule is actually a short cut from making a lot more calculus in a specific exercise.

The examples below will make you fully understand the rule:
product rule for exponents

As you can see in the example, the product rule exponents simply too to each other and the base remain unchanged. A more advanced rule named the ”Power Rule" says that if you want to raise a power to a number, you only have to multiply the exponents. In the following example you will see the general form of the rule and the fact that 52 raised to the 3rd power s equals 56.
product rule exponents

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