Powers of zero | Exponents, radicals, and scientific notation | Pre-algebra | Khan Academy

TL;DR

Powers of zero in exponentiation result in zero except for zero to the zeroth power, which is a contested concept.

Transcript

• [Instructor] In this video, we're going to talk about powers of zero. And just as a little bit of a reminder, let's start with a nonzero number, just to remind ourselves what exponentiation is all about. So if I were to take two to the first power, one way to think about this is we always start with a one, and then we multiply this base that many... Read More

Key Insights

• #️⃣ Exponentiation involves multiplying a base number by itself a certain number of times.
• ✊ Any number to the power of zero equals one, except for zero to the zeroth power.
• 0️⃣ Zero to the first power is always zero, and zero to any positive exponent equals zero.

Questions & Answers

Q: What is exponentiation and how does it work with nonzero numbers?

Exponentiation involves multiplying a base number by itself a certain number of times. For example, 2 to the power of 3 means multiplying 2 by itself three times (2 * 2 * 2 = 8).

Q: What is two to the zero power and why?

Two to the zero power is equal to one. This is because exponentiation starts with a base of one and the number is multiplied by itself zero times, resulting in just one.

Q: What is zero to the first power, and what does it equal?

Zero to the first power is equal to zero. This is because when zero is multiplied by itself once, the product becomes zero.

Q: What is the controversy surrounding zero to the zeroth power?

There are different opinions about what zero to the zeroth power should be. Some argue that it should be one, based on the exponentiation pattern. Others believe it should be undefined or zero, considering the base value being zero.

Summary & Key Takeaways

• Exponentiation involves multiplying a base number by itself a certain number of times.

• Any number to the power of zero equals one, except for zero to the zeroth power, which is undefined or equal to one depending on interpretation.

• Zero raised to any positive value exponent always equals zero.