Bases and Powers – The Language of Exponents

Every exponent expression has two parts and one name for the whole thing: in 6⁴, the base is 6 (the number being multiplied), the exponent (or index) is 4 (how many times it's multiplied), and 6⁴ as a whole is called a power. Getting this vocabulary solid now makes every exponent rule covered later in this section far easier to follow – “the power of a power” and “multiplying powers” only make sense once base, exponent, and power are second nature.

Naming the Parts

In bⁿ: b is the base, n is the exponent, and bⁿ together is called a power.

In the expression 9³, identify the base and the exponent.

The base is 9 (the number being multiplied). The exponent is 3 (how many times it's multiplied by itself).

Converting Between Forms

Write 4 × 4 × 4 × 4 × 4 using exponent notation.

4 is multiplied by itself 5 times: 4⁵.

Real-Life Application

Reading formulas: scientific and engineering formulas are full of powers.
Computer science: base 2 underlies almost all digital technology.
Finance: compound interest formulas use powers of (1 + rate).

Key Takeaways

Base = the number being multiplied; exponent = how many times; power = the whole expression.
Repeated multiplication of the same number converts directly into exponent form.
This vocabulary is the foundation for every exponent law covered later in this section.

Practice: Bases and Powers

Write in Exponent Form