QUOTIENTS OF MONOMIALS
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Unit Overview
In this unit, you will learn how to simplify ratios involving monomials. This is useful in biology, physics, and using scientific notation. The unit will conclude with negative exponents which are used to represent very small numbers.
Dividing Monomials
When simplifying quotients, you can do so by first expressing the powers in terms of their factors. Take a look at the example below and see if you can derive a rule on how to simplify monomial quotients.
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Did you figure out a rule for dividing monomials? If you said that you can subtract the exponents, you are correct. Study the property below.
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Notice in the property above that the exponent is given to the term in the numerator and the term in the denominator. Let’s take a look at some examples involving this property.
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Stop! Go to Questions #1-16 about this section, then return to continue on to the next section.
Negative Exponents
Negative exponents are used to represent very small numbers. Study the property defining negative exponents below.
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*All properties from this unit and any previous units will also apply to negative exponents.
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If an exponent is negative in the numerator, the base will be moved to the denominator to make the exponent positive. If an exponent is negative in the denominator, the base will be moved to the numerator to make the exponent positive.
Let’s take a look at an example of the statement above.
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Zero as an Exponent
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The property illustrated above shows us that any number to the zero power is equal to 1.
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Stop! Go to Questions #17-44 to complete this unit.
