What you’ll learn
Understand zero exponent.
Key idea
A nonzero number divided by itself has multiplicative identity value, not zero.
The zero-exponent rule requires nonzero base; no assertion about zero to the zero power.
Worked example
Classify examples and non-examples for the concept 'Understand zero exponent'.
For nonzero base -17, classify claim (-17)^0=1, using quotient (-17)^4/(-17)^4 as evidence.
- Base -17 is nonzero; (-17)^4=83521 is nonzero too.
- Dividing this power by itself gives (-17)^(4-4)=(-17)^0=1. Descending from (-17)^1=-17, divide by -17 to get 1.
Answer: True — the quotient of nonzero 83521 by itself is 1, so (-17)^0=1.
Quick Check
Classify examples and non-examples for the concept 'Understand zero exponent'.
For nonzero base -10, classify claim (-10)^0=1, using quotient (-10)^1/(-10)^1 as evidence.