Lecture on Exponents

Introduction

• Second video on exponents.
• Introduction to negative exponents and exponents on fractions.

Review of Basic Exponents

• Example: 3 squared (3^2) = 9
• 3 multiplied by itself two times: 3 x 3 = 9

Negative Exponents

Misconception

• Natural logic: Positive exponent results in a positive number; negative exponent results in a negative number. This is incorrect.

Solving Negative Exponents

• Rule: A negative exponent in the numerator becomes a positive exponent in the denominator.
• Example: 3^(-2)
  • Rewrite: 1 x 3^(-2)
  • Solution: 1 / (3^2) = 1 / 9

Negative Exponent in the Denominator

• Rule: A negative exponent in the denominator becomes a positive exponent in the numerator.
• Example: 1 / 3^(-2)
  • Rewrite: 3^2
  • Solution: 3 x 3 = 9

Negative Numbers with Negative Exponents

• Example: 6 x (-3)^(-2)
  • Rewrite: 6 / (-3)^2
  • Simplified: Negative 3 multiplied by itself: (-3) x (-3) = 9
  • Simplified Fraction: 6 / 9 = 2 / 3

Fractions with Negative Exponents

• Example: (3/4)^(-2)
  • Multiply by 1: 1 x (3/4)^(-2)
  • Rewrite: 1 / (3/4)^2
  • Simplified: (3/4) x (3/4) = 9/16
  • Final Simplification: 1 / (9/16) = 16/9

Conclusion

• Clarification on negative exponents in fractions.
• Preview: Next video will cover properties of exponents.
• Encouragement to stay tuned for more videos.