Exponents Are a Kind of Shorthand
Many numbers are the product of the same factor multiplied over and over again. For example, 32 = 2 × 2
× 2 × 2 × 2. Another way to write this would be 32 = 2^5 , or “thirty-two equals two to the fifth power.”
The little number, or exponent, denotes the number of times that 2 is to be used as a factor. In the same
way, 10^3 = 10 × 10 × 10, or 1,000, or “ten to the third power,” or “ten cubed.” In this example, the 10 is
called the base and the 3 is called the exponent. (You won’t need to know these terms on the SAT, but you
will need to know them to follow our explanations.)
Exponents and Your Calculator
Raising a number to a power is shown in two different ways on your calculator, depending on the
type of calculator you have. A scientific calculator will use the yx button. You’ll have to type in your
base number first, then hit the yx key, and then type the exponent. So 4^3 will be typed in as “4 yx 3 =”
and you’ll get 64. If you have a calculator from the TI-80 series, your button will be a ^ sign. You’ll
enter the same problem as “4^3 [ENTER].” Think of these two keys as the “to the” button, because
you say “4 to the 3rd power.”Multiplying Numbers with Exponents
When you multiply two numbers with the same base, you simply add the exponents. For example, 2^3 × 2^5
= 23+5 = 2^8.
Warning
The rules for multiplying
and dividing exponents
do not apply to addition
or subtraction:
22 + 2^3 = 12
(2 × 2) + (2 × 2 × 2) = 12
It does not equal 2^5 or 32.Dividing Numbers with Exponents
When you divide two numbers with the same base, you simply subtract the exponents. For example, =
2 5-3 = 2^2.
Raising a Power to a Power
When you raise a power to a power, you multiply the exponents. For example, (2^3 )^4 = 23 × 4 = 2^12.
Warning
Parentheses are very
important with exponents,
because you must
remember to distribute
powers to everything