Lecture Notes on Powers and Indices

Recommended Pre-requisite Videos

• Squaring a Number
• Square Numbers
• Cubing a Number
• Cubed Numbers

Basic Concepts

• Definition of Power/Index: Represents how many times a number (base) is multiplied by itself.
  • Example: 5² means 5 multiplied by itself (5 x 5 = 25).
  • The number 2 in 5² is called a power or an index.

Special Terminology

• Squared: A number raised to the power of 2.
• Cubed: A number raised to the power of 3.

Calculation Examples

• Two to the Power of Four (2⁴):
  • Calculation: 2 x 2 x 2 x 2 = 16
• Ten to the Power of Five (10⁵):
  • Calculation: 10 x 10 x 10 x 10 x 10 = 100,000
• Two to the Power of Six (2⁶):
  • Calculation: 2 x 2 x 2 x 2 x 2 x 2 = 64

Evaluating Powers

• You may be asked to evaluate powers or write them in an expanded form.
  • Example: 10⁵ as 10 x 10 x 10 x 10 x 10
• For large numbers, it's practical to use a calculator.

Using a Calculator for Powers

• Identifying Power Buttons: Locate the power button, often denoted as xⁿ.
  • Specific buttons for squared (x²) and cubed (x³) are available, but xⁿ is used for other powers.

Calculator Examples

• 7 to the Power of 5 (7⁵):
  • Use power button: 7 xⁿ 5 = 16,807
• 6 to the Power of 10 (6¹⁰):
  • Result: 60,466,176
• 1 to the Power of 250:
  • Result: 1 (since multiplying 1 by itself any number of times results in 1)
• 2.5 to the Power of 4 (2.5⁴):
  • Result: 39.0625

Key Takeaway

• The power button on calculators is extremely useful for efficiently calculating powers, especially for large numbers.