Exponents and Radicals: The Basics

An exponent is the small raised number. It tells you how many times to multiply the base by itself, so $2^{3}$ means $2 \times 2 \times 2 = 8$.

Most SAT questions on this topic come down to four rules. When you multiply powers with the same base, add the exponents. When you divide them, subtract the exponents. When a power is raised to another power, multiply the exponents. And anything raised to the zero power equals $1$.

A square root asks which number times itself gives you the number under the symbol, so $\sqrt{36} = 6$. A negative exponent does not make an answer negative — it means one over that power, so $3^{-2} = \frac{1}{9}$. A fraction exponent is a root: $x^{1/2} = \sqrt{x}$.

Know the rules and the small square roots by sight, and these questions become quick.