Exponent & Powers Explorer

Enter a base and exponent to see the expanded multiplication, visual area or volume model, and a powers table. The tool handles zero exponents, negative exponents, and large powers.

Base

raised to

Exponent

Try negative exponents (like -3) or zero. Base and exponent update results instantly.

Try an example

Result

2⁴ = 16

Expanded Form

2^{4} = 2 \times 2 \times 2 \times 2

= 2 \to 4 \to 8 \to 16

2^{4} = 16

Repeated Multiplication

2x2x2x2=16

Powers of 2

Expression	Expanded	Value
2⁰	1	1
2¹	2	2
2²	2 x 2	4
2³	2 x 2 x 2	8
2⁴	2 x 2 x 2 x 2	16
2⁵	2 x 2 x 2 x 2 x 2	32
2⁶	2 x 2 x 2 x 2 x 2 x 2	64

Reference Guide

What Exponents Mean

An exponent tells you how many times to multiply a number by itself. The number being multiplied is the base and the small raised number is the exponent (or power).

2^4 = 2 \times 2 \times 2 \times 2 = 16

We say "2 to the fourth power" or "2 raised to 4." Squaring ( $n^2$ ) means multiplying a number by itself once. Cubing ( $n^3$ ) means multiplying three times.

Square and Cube Numbers

Square numbers form a square grid. $3^2 = 9$ means a 3 by 3 grid of 9 unit squares. The first few perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Cube numbers form a 3D block. $2^3 = 8$ means 2 layers of a 2 by 2 grid = 8 unit cubes. The first few perfect cubes are 1, 8, 27, 64, 125, 216.

Special Exponents

Zero exponent

Any nonzero number raised to 0 equals 1. $5^0 = 1$ , $100^0 = 1$ .

Exponent of 1

Any number raised to 1 is just itself. $7^1 = 7$ .

Negative exponent

A negative exponent means "take the reciprocal." $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$ .

Powers of 10

Powers of 10 are especially important because our number system is base 10. The exponent tells you how many zeros to write after the 1.

10^1 = 10,\quad 10^2 = 100,\quad 10^3 = 1{,}000

This connects directly to place value: $10^3$ is the thousands place, $10^6$ is the millions place. Scientific notation uses powers of 10 to write very large or very small numbers compactly.