What you’ll learn
Understand negative integer exponents.
Key idea
For a nonzero base, negative integer exponents denote reciprocals of the corresponding positive powers.
A negative exponent creates a reciprocal, not a negative sign or a vanished value.
Worked example
Classify examples and non-examples for the concept 'Understand negative integer exponents'.
Classify statement (3)^(-3)=1/27, with reciprocal evidence.
- For nonzero base 3, (3)^(-3) is reciprocal of (3)^3=27, hence 1/27.
- Descending from exponent 4 to -3 divides by 3 at every step; a negative exponent changes magnitude by reciprocal, not sign.
Answer: True — (3)^(-3)=1/(3)^3=1/27.
Quick Check
Classify examples and non-examples for the concept 'Understand negative integer exponents'.
Classify statement (6)^(-1)=-6, with reciprocal evidence.