Intro to Exponents

Key Concepts

• Exponent: Indicates how many times a number (the base) is multiplied by itself.
• Base: The larger number which is multiplied by itself.
• Exponential Form: Written as base^exponent (e.g., 5²).
• Expanded Form: Writing out the multiplication (e.g., 5² is 5 * 5).

Examples

Example 1: 5²

• Base: 5
• Exponent: 2
• Calculation: 5 * 5 = 25
• Common Mistake: Not 5 * 2
• Ways to Say:
  • 5 to the power of 2
  • 5 to the second power
  • 5 squared (special name for exponent 2)

Example 2: 5³

• Base: 5
• Exponent: 3
• Calculation: 5 * 5 * 5 = 125
• Ways to Say:
  • 5 to the power of 3
  • 5 to the third power
  • 5 cubed (special name for exponent 3)

Example 3: 3⁶

• Base: 3
• Exponent: 6
• Expanded Form: 3 * 3 * 3 * 3 * 3 * 3
• Calculation Strategy:
  • Pairing method: (33) * (33) * (3*3) = 9 * 9 * 9 = 81 * 9 = 729
  • Alternative method: Multiply sequentially (3 * 3 = 9, 9 * 3, etc.)
• Final Answer: 729

Example 4: 9²

• Base: 9
• Exponent: 2
• Calculation: 9 * 9 = 81

Example 5: 2⁵

• Base: 2
• Exponent: 5
• Expanded Form: 2 * 2 * 2 * 2 * 2
• Calculation:
  • 2 * 2 = 4
  • 4 * 2 = 8
  • 8 * 2 = 16
  • 16 * 2 = 32
• Final Answer: 32

Example 6: 7⁴

• Base: 7
• Exponent: 4
• Expanded Form: 7 * 7 * 7 * 7
• Calculation Strategy:
  • Pairing method: (77) * (77) = 49 * 49
  • 49 * 49 = 2401
• Final Answer: 2401

Conclusion

• An exponent shows the repeated multiplication of a base number.
• Important terms include base, exponent, expanded form, and special names like squared (power 2) and cubed (power 3).
• Various strategies can be used to simplify large exponents.