There are some instances where exponents are either zero or a negative number. They follow a special set of rules that can be used to evaluate expressions.
Zero and Negative Exponents
|A nonzero number raised to the zero power is equal to 1.|
|A nonzero number raised to a negative power is the reciprocal of that number raised to the opposite of the power.|
|Zero raised to any positive power is zero.|
|Zero to the zero power is generally defined as 1.
In certain contexts, however, is referred to as an indeterminate form. So, a calculator may show it as undefined.
|Zero raised to a negative power is undefined.|
Rules of Exponents
To simplify expressions containing exponents, it may be helpful to look at some expressions written in expanded form.When an exponential expression is expanded and multiplied, exponents are added:
Properties of Exponents
|Product of powers property||To multiply two powers with the same base, add the exponents.|
|Power of a product property||To raise a product to a power, raise both factors to the power.|
|Quotient of powers property||To divide two powers with the same base, subtract the exponents.|
|Power of a quotient property||To raise a quotient to a power, raise both expressions to the power.|
|Power of a power property||To raise a power to a power, multiply the exponents.|
Simplify the power . Multiply the exponents.Use the power of a product property to write as .