What Happens When You Raise 1 and -1 to Powers?

TL;DR

Raising 1 to any power will always result in 1, including 1 to the 0 power, which is generally accepted as 1 despite some debate. In contrast, raising -1 to an even power yields 1, while raising it to an odd power results in -1, creating an alternating pattern based on the parity of the exponent.

Transcript

Let's think about exponents with ones and zeroes. So let's take the number 1, and let's raise it to the eighth power. So we've already seen that there's two ways of thinking about this. You could literally view this as taking eight 1's, and then multiplying them together. So let's do that. So you have one, two, three, four, five, six, seven, eight ... Read More

Key Insights

• ✊ Raising 1 to any power will always be 1.
• ✊ 1 to the 0 power is debatable and may be considered either 1 or undefined.
• ✊ Negative 1 raised to an even power is always 1, while negative 1 raised to an odd power is always -1.
• ✊ The pattern of alternating between 1 and -1 for negative 1 powers is due to the even or odd nature of the exponent.

Questions & Answers

Q: What is the result of raising 1 to any power?

Raising 1 to any power will always result in 1. This is because multiplying 1 by itself any number of times will still yield 1.

Q: What is 1 to the 0 power equal to?

The value of 1 to the 0 power is a topic of debate. Some argue that it should be 1 based on the pattern of other exponents, while others argue that it is undefined.

Q: What is the pattern of negative 1 raised to different powers?

Negative 1 raised to an even power will always result in 1, while negative 1 raised to an odd power will be -1. This pattern repeats for higher powers.

Q: What is the result of raising negative 1 to a large even power?

Raising negative 1 to a large even power will always be 1. The number of negatives in the multiplication cancels out and results in a positive value.

Summary & Key Takeaways

• Exponents of 1 always result in 1, regardless of the exponent.

• 1 to the 0 power is generally considered to be 1, although there is some debate.

• Exponents of negative 1 alternate between 1 and -1 based on whether the power is even or odd.