## SAT SUBJECT TEST MATH LEVEL 1

## TOPICS IN ARITHMETIC

## CHAPTER 2

Basic Arithmetic

### EXPONENTS AND ROOTS

In the expression *b ^{n}*, which is read “

*b*to the

*n*th,” “

*b*to the

*n*th power,” or “

*b*raised to the

*n*th power,”

*b*is called the

**and**

*base**n*is called the

**. Almost all of the exponents that appear in questions on the Math 1 test are integers. Integer exponents are defined in the next KEY FACT.**

*exponent***Key Fact A10**

**For any number b**

**and positive integer**

*n*:• **if b**

**0, then**=

*b*^{0}**1**

• ** b^{1}**=

*b*• **if n** >

**1, then where**

*b***is a factor**

*n***times**

•

For example,

Several rules govern the use of exponents in mathematics. The most important ones are listed in the next KEY FACT.

**Key Fact A11**

**LAWS OF EXPONENTS**

**For any numbers b**

**and**

*c***and integers**

*m***and**

*n*:• *b ^{m}b^{n}*

**=**

*b*^{m+n}•

• (** b^{m}**)

^{n}**=**

*b*^{mn}• *b ^{m}c^{m}*

**=**(

**)**

*bc*

^{m}**TIP**

Memorize the laws of exponents. They come up quite often on the Math 1 test.

For example,

**EXAMPLE 2:** If 4* ^{m}* 4

*= 4*

^{n}^{10}, what is the average (arithmetic mean) of

*m*and

*n*?

Since 4* ^{m }* 4

*= 4*

^{n }

^{m}^{+n}: