Module_06 // Powers
POWERS &
EXPONENTS
Multiplication is a shortcut for addition. Exponents are a shortcut for multiplication. They allow us to write, calculate, and understand numbers that grow incredibly fast.
Anatomy of a Power
4
The Base
3
The Exponent
Step 1: Look at the Base. That is the number you are going to copy.
Step 2: Look at the Exponent. That tells you exactly how many copies to make.
Step 3: Multiply them all together!
4 × 4 × 4 = 64
Squared ( x² )
Named after finding the 2D Area of a Square.
Cubed ( x³ )
Named after finding the 3D Volume of a Cube.
Interactive Lab
The Power Visualizer
Base Number2
The Modifier (n)3
Multiplication
2 × 3
2 + 2 + 2
= 6
Exponentiation
2 3
2 × 2 × 2
= 8
Scale Comparison
6
Linear
8
Exponent
Scientific Notation
Scientists study things that are massive (galaxies) and tiny (atoms). Writing 20 zeros takes too long. Exponents let us package zeros up into a small, easy-to-read number.
Standard FormScientific Notation
3,200,0003.2 × 106
Verification Protocol
Knowledge Check: Powers1 / 3
What does 3⁴ mean mathematically?
Rule Mastery
You have harnessed the power of exponential growth.