SAT SUBJECT TEST MATH LEVEL 1
TOPICS IN 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
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:
• bmbn = bm+n
• (bm)n = bmn
• bmcm = (bc)m
Memorize the laws of exponents. They come up quite often on the Math 1 test.
EXAMPLE 2: If 4m 4n= 410, what is the average (arithmetic mean) of m and n?
Since 4m 4n = 4m+n: