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Chapter 4

Making Exponential Expressions and Operations More Compatible

An exponential expression consists of a base and a power. The general format of an exponential expression is bⁿ, where b is the base and n is the power or exponent. The base, b, has to be a positive number, and the power, n, is a real number. Positive powers, negative powers, and fractional powers all have special meanings and designations.

The Problems You’ll Work On

Here are some of the things you do in this chapter:

 Multiplying and dividing exponential factors with the same base

 Raising a power to a power — putting an exponent on an exponential expression

 Combining operations — deciding what comes first when multiplying, dividing, and raising to powers

 Changing numbers to the same base so they can be combined

 Writing numbers using scientific notation

What to Watch Out For

Be sure you also remember the following:

 Writing fractional expressions by using the correct power of a base

 Recognizing a common base in different numbers

 Remembering when to add, subtract, and multiply the exponents

 Using the correct power of ten in scientific notation expressions

Multiplying and Dividing Exponentials with the Same Base

141–150 Perform the operations and simplify.

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Raising a Power to a Power

151–160 Compute the powers and simplify your answers.

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Combining Different Operations on Exponentials

161–170 Use the order of operations to compute the final answers.

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Changing the Base to Perform an Operation

171–180 Perform the operations by changing the numbers to the same base.

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Working with Scientific Notation

181–190 Perform the operations on the numbers written in scientific notation. Write your answer in scientific notation.

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