SAT SUBJECT TEST MATH LEVEL 1

TOPICS IN ARITHMETIC

CHAPTER 2
Basic Arithmetic

EXPONENTS AND ROOTS

In the expression bⁿ, which is read “b to the nth,” “b to the nth power,” or “b raised to the nth power,” b is called the base and n is called the exponent. 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.

Key Fact A10

For any number b and positive integer n:

• if b 0, then b⁰= 1

• b¹= 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^mbⁿ = b^m+n

•

• (b^m)ⁿ = b^mn

• b^mc^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 4ⁿ= 4¹⁰, what is the average (arithmetic mean) of m and n?

Since 4^m 4ⁿ = 4^m+n: