Exponents and Roots

In the expression $b^n$, 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 bⁿ = b · b · b · · · b, where b is a factor n times.
• ${\mathit{b}}^{-\mathit{n}}={\displaystyle \frac{1}{{\mathit{b}}^{\mathit{n}}}}$.

For example,

$\begin{array}{rllcccl}{4}^0& =& 1& & & & 4^4=4\times 4\times 4\times 4=256\\ 4^1& =& 4& & & & 4^{-1}=\frac{1}{4^1}=\frac{1}{4}\\ 4^2& =& 4\times 4=16& & & & 4^{-2}=\frac{1}{4^2}=\frac{1}{16}\end{array}$

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

Key Fact A11