Multiplying –1 by itself repeatedly is a classic math trick that plays with signs. If you multiply –1 × –1, the result is +1. But what if you do it 100 times?
The Math Behind It
Let’s break it down step by step:
Step 1: Understand the Pattern
Whenever you multiply an even number of negative ones, the product is +1.
Whenever you multiply an odd number of negative ones, the product is –1.
Step 2: What Is 100?
100 is an even number.
Step 3: Final Answer
(–1)100=+1(–1)^{100} = +1(–1)100=+1
✅ So, the product is: +1
Quick Recap
- (–1) × (–1) = +1
- (–1) × (–1) × (–1) = –1 (odd times = negative)
- (–1) × (–1) × (–1) × (–1) = +1 (even times = positive)
When Is This Useful?
- Algebra and exponents
- Sign rule questions in exams
- Fast mental math tricks
💡 Tip: Just remember:
Even exponent → Positive (+1)
Odd exponent → Negative (–1)