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Quotient of Powers Rule

This is the formula for the Quotient of Powers Rule:

Now let's talk about what it means. The Quotient of Powers Rule assists with simplifying exponents. Let's first define some terms as they relate to exponents. When you have a number or variable raised to a power, the number (or variable) is called the base, while the superscript number is called the exponent or power.

In a division problem involving exponents, if the bases are the same, the problem can be simplified by subtracting the exponents. For example, take this problem: m^5 / m^3 = ?. Because the base ( m) is the same, you can simplify this problem by subtracting the exponents: 5 - 3 = 2. Therefore m^5 / m^3 = m^2.

Here is how this works.

Every m / m is equal to 1 and can be canceled out. For this problem, there are three of those 'sets,' which leave us with two ms in the numerator of the fraction. This simplifies to m^2.

Examples

You can use the Quotient of Powers Rule for simple or complex division problems. Let's do a few practice ones together. If you need more time to work them out, try pausing the video before you see the answers.

First, let's simplify f^7 / f^2.

Since the bases are the same, to solve this problem, just subtract the exponents. You should have gotten f^7 / f^2 = f^5 since 7 - 2 = 5.

You can only combine like terms. Those are the terms with the same bases. If it helps you to rearrange the problem so that terms with like bases are together, no problem. Just don't leave anything out. When you rearrange the terms, you get the following:

Then, just subtract the exponents for each term:

When you put it all together, the answer is ab^3 c.

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quotient of powers: property & examples - video & lesson transcript | study.com

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Quotient Of Powers: Property & Examples - Video & Lesson Transcript | Study.com

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This is the formula for the Quotient of Powers Rule: Now let's talk about what it means. The Quotient of Powers Rule assists with simplifying exponents. Let's first define some terms as they relate to exponents.

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Quotient of Powers Property | Mathematics

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Rules of Exponents Quotient of Powers Property

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This video tutorial will show you an example of how to use the Quotient of Powers Property.