Exponents

What is an exponent?

An exponent is a short way to write repeated multiplication. In the power 2³, the small raised number (the exponent) tells you how many times to multiply the big number (the base) by itself: 2³ means 2 × 2 × 2 = 8. Instead of writing the same factor over and over, an exponent packs it into two small numbers.

Base vs. exponent

• Base — the number being multiplied (the factor that repeats).
• Exponent — how many times the base is used as a factor.
• So 3⁴ = 3 × 3 × 3 × 3 = 81 — a base of 3 used four times, not 3 × 4.

How to use this tool

• Set the base (2–10) and the exponent (0–6).
• Press Play to build the product one factor at a time and hear the chain read aloud.
• Use Step to move one multiplication at a time, and Replay to start over.
• Watch the growth chart: each bar is the next power, so you can see the value shoot up.

Why powers grow so fast

Multiplying by the base again and again is called exponential growth. Each step doesn’t just add a little — it multiplies, so the totals pull away from a straight line quickly. Doubling (base 2) reaches 64 in only six steps, and a base of 10 races to a million. Seeing the bars leap upward makes that “gets big fast” idea concrete.

One more surprise the tool shows: any base raised to the power 0 equals 1, because you have multiplied the base zero times and are left with the starting value, 1.

Good for

Grades 6–9 — introducing exponents and powers, connecting them to repeated multiplication, and building intuition for exponential growth before pre-algebra and algebra.