Introduction to Exponents

Definition

• Exponent: A small number placed to the upper right of a base number indicating how many times the base is multiplied by itself.
• Base: The larger number that is being multiplied.

Examples Explained

Example 1: 5 to the power of 2

• Expression: (5^2)
• Base: 5
• Exponent: 2
• Meaning: Multiply the base (5) by itself twice: (5 \times 5 = 25)
• Common Mistake: Thinking (5^2) equals (5 \times 2)

How to say it

• 5 to the power of two
• 5 to the 2 power
• 5 squared (special name for exponent of two)

Example 2: 5 to the power of 3

• Expression: (5^3)
• Meaning: Multiply the base (5) by itself three times: (5 \times 5 \times 5 = 125)
• Names:
  • 5 to the power of three
  • 5 to the 3 power
  • 5 cubed (special name for exponent of three)

Example 3: Expanded form to Exponential form

• Expression: (3 \times 3 \times 3 \times 3 \times 3 \times 3)
• Exponential Form: (3^6)
• Calculation:
  • Pairing: ((3 \times 3) \times (3 \times 3) \times (3 \times 3) = 9 \times 9 \times 9 = 729)

Example 4: 9 squared

• Expression: (9^2)
• Meaning: (9 \times 9 = 81)

Example 5: 2 to the 5th power

• Expression: (2^5)
• Meaning: Multiply the base (2) by itself five times:
  • Breakdown: (2 \times 2 = 4)
  • (4 \times 2 = 8)
  • (8 \times 2 = 16)
  • (16 \times 2 = 32)

Example 6: 7 to the 4th power

• Expression: (7^4)
• Meaning: Multiply the base (7) by itself four times:
  • Pairing: ((7 \times 7) = 49)
  • (49 \times 49 = 2,401)

Conclusion

• Exponents signify repeated multiplication of a base by itself.
• Special terminology for powers of 2 (squared) and 3 (cubed).
• Various methods can be used to compute the final values.

End of lecture summary on the introduction to exponents.