Adding/Subtracting Fractions with Variables and Exponents Help
Adding/Subtracting Fractions with Variables and Exponents
When adding fractions with variables in one or more denominators, the LCD will have each variable (or algebraic expression) to its highest power as a factor. For example, the LCD for is x 2 y 3 .
Find practice problems and solutions at Adding/Subtracting Fractions: Practice Problems - Set 1.
Exponent Properties 5 & 6 - Adding/Subtracting Fractions with Variables and Negative Exponents
Property 5 - Negative Exponents
This property says that a –1 is the reciprocal of a . In other words, a –1 means “invert a .”
(Review Exponent Properties 1-4)
Property 6 - Negative Exponents Other than One
This is a combination of Properties 3 and 5: .
Often a combination of exponent properties is needed. In the following examples the goal is to rewrite the expression without using a negative exponent.
Find practice problems and solutions at Adding/Subtracting Fractions: Practice Problems - Set 2.
Exponent Properties 7 & 8 - Adding/Subtracting Fractions with Variables and Exponents with Products and Quotients
In expressions such as (2 x ) –1 the exponent “–1” applies to 2 x , but in 2 x –1 the exponent “–1” applies only to x :
Property 7 - Power of Products
( ab) n = a n b n
By Property 7 we can take a product then the power or take the powers then the product.
It is not true that (a + b) n = a n + b n . This mistake is very common.
Property 8 - Property of Quotients
Property 8 says that we can take the quotient first then the power or each power followed by the quotient.
This example will be used for the rest of the examples and practice problems.
This expression can be simplified more quickly using Property 8 and Property 3. (Review Exponent Properties 1-4)
Find practice problems and solutions at Adding/Subtracting Fractions Practice Problems - Set 3.
More practice problems for this concept can be found at: Exponents and Roots Practice Test.