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You combine exponents with different signs by using the rules for adding and subtracting signed numbers. Fractional exponents are combined after finding common denominators. Exponents that are improper fractions are left in that form.

Try going through many of the situations that could arise when distributing, such as distributing both a number and a variable, distributing various powers of more than one variable, distributing negatives, rewriting negative exponents as fractional terms, distributing fractional powers, and distributing radicals. This touches on just about anything you’d probably come across.

The basic type of exponential equation has a variable on only one side and can be written with the same base for each side. For example, if you’re asked to solve 4^{ – 2} = 64, you follow these steps:

If you must solve an equation with variables on both sides, you have to do a little more work (sorry!). For example, to solve 2^{ – 5} = 8^{ – 3}, follow these steps:

Whether an exponential equation contains a variable on one or both sides, the type of equation you’re asked to solve determines the steps you take to solve it.

The next example contains negative powers and fractional powers — the rules for exponents remain the same with negative and fractional exponents.

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For example, the preceding statements can be recoded as follows: Since SAS evaluates quantities inside parentheses before performingany operations, the expressions and are evaluated first and the result (1 or 0) is substituted for the expressionsin parentheses.

Distributing variables over the terms in an algebraic expression involves multiplication rules and the rules for exponents. When different variables are multiplied together, you can write them side by side without using any multiplication symbols. If the same variable is multiplied as part of the distribution, then you add the exponents.

The followingare examples of prefix operators used with variables, constants, functions,and parenthetic expressions:An **infix operator** applies to the operands on each sideof it, for example, 6

Combine the variables with the same base using the rules for exponents. The signs of the results follow the rules for multiplying signed numbers.

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