**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} .

**Examples**

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)

**Examples**

**Property 6 - Negative Exponents Other than One**

This is a combination of Properties 3 and 5: .

**Examples**

Often a combination of exponent properties is needed. In the following examples the goal is to rewrite the expression without using a negative exponent.

**Examples**

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.

**Examples**

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.

**Examples**

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.

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