Exponents & Scientific Notation

Exponents are a compact way to show repeated multiplication, and scientific notation uses exponents to write very large or very small numbers efficiently. These ideas appear in algebra, physics, chemistry, computer science, and everyday calculations involving scale. Learning the rules of exponents helps students simplify expressions quickly and avoid long arithmetic. Scientific notation also makes it easier to compare quantities like the size of atoms or the distance to stars.

An exponent tells how many times a base is multiplied by itself, such as $2^4 = 2 \times 2 \times 2 \times 2$. The exponent rules let us combine, divide, and raise powers without expanding every factor. Scientific notation writes a number as $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer. Positive exponents move the decimal to the right in value, while negative exponents represent numbers less than $1$.