Powers of Numbers Table
Visualize the geometry of growth. Explore Squares (n²), Cubes (n³), and higher dimensions.
Power Explorer
See how fast a number grows when multiplied by itself repeatedly.
Did you know?
2² is called a "Square" because it calculates the area of a square with side length 2.
2³ is called a "Cube" because it calculates the volume of a cube with side length 2.
The Geometry of Powers
Numbers aren't just abstract symbols; they represent shapes in our world. The words "Squared" and "Cubed" come directly from geometry.
The Square (n²)
Think of a floor tile. If it's 2 feet wide and 2 feet long, the area is 4 square feet. Squaring maps a number to a 2D area.
The Cube (n³)
Think of a box. If it's 2ft wide, 2ft long, and 2ft tall, the volume is 8 cubic feet. Cubing maps a number to a 3D volume.
Hyper-Growth (n⁴+)
Beyond cubes, we leave 3D space. n⁴ is often used in physics for things like thermal radiation power (Stefan-Boltzmann law).
Important Powers to Memorize
Knowing these by heart will make algebra much faster for you.
Top 5 Perfect Squares
- 1² 1
- 2² 4
- 3² 9
- 4² 16
- 5² 25
Top 5 Perfect Cubes
- 1³ 1
- 2³ 8
- 3³ 27
- 4³ 64
- 5³ 125
Frequently Asked Questions
Why is n² called a 'Square'?
It's geometric! If you have a square shape with side length n, its Area is n × n = n². So 5² is literally the area of a 5x5 square.
Why is n³ called a 'Cube'?
Similarly, if you have a 3D Cube with side length n, its Volume is n × n × n = n³. So 5³ is the volume of a 5x5x5 cube.
What is a 'Perfect Square'?
A perfect square is a number that is the result of squaring an integer. 1, 4, 9, 16, 25 are perfect squares (because 1², 2², 3², 4², 5²).
What comes after Squared and Cubed?
We usually just say 'to the power of 4', 'to the power of 5', etc. In geometry, n⁴ would be a 'Tesseract' (4D Hypercube), but that's hard to visualize!
Do powers grow faster than multiplication?
Yes, much faster. 10 × 2 is 20. But 10² is 100. As numbers get bigger, the difference becomes enormous.
What is any number to the power of 1?
Any number to the power of 1 is itself. n¹ = n. It means you have one copy of the number.
What about negative numbers?
A negative number squared is positive (-2 × -2 = 4). But a negative number cubed is negative (-2 × -2 × -2 = -8). The sign flips for odd powers.
What is the fast way to calculate powers of 10?
Just count the zeros! 10³ has 3 zeros (1,000). 10⁶ has 6 zeros (1,000,000). The exponent matches the number of zeros.
How do I use this table?
Find your number 'n' in the left column. Read across to see its Square (n²), Cube (n³), and higher powers. Use the 'Explorer' tab to calculate custom values.
What is n⁰?
For any non-zero number n, n⁰ = 1. This is a fundamental rule of exponents.