Understanding Base and Index

1. Read & Understand

Every exponent has two parts:

• Base = the number being multiplied

• Index (Exponent) = how many times it is multiplied

Example:
2³ = 2 × 2 × 2 = 8

• Base = 2

• Index = 3

Think of the base as the “building block” and the index as the “instruction.”

2. Try It Yourself

Identify the base and index:

1. 5² → Base = ___, Index = ___

2. 7³ → Base = ___, Index = ___

3. 10⁴ → Base = ___, Index = ___

4. x⁵ → Base = ___, Index = ___

3. Real-World Connection

• In 4² = 16, base = side length, index = multiply twice for area.

• In 2¹⁰ = 1024, base = doubling unit, index = number of doublings.

4. Watch Out for Mistakes

• In 3⁴, base is 3, not 4

• Don’t confuse repeated multiplication with the base itself