Negative exponents | Exponents, radicals, and scientific notation | Pre-Algebra | Khan Academy

TL;DR

Negative exponents are interpreted as reciprocals, and by applying this principle, we can solve problems involving negative exponents.

Transcript

We already know that 2 to the fourth power can be viewed as starting with a 1 and then multiplying it by 2 four times. So let me do that. So times 2, times 2, times 2, times 2. And that will give us, let's see, 2 times 2 is 4, 8, 16. So that will give us 16. Now I will ask you a more interesting question. What do you think 2 to the negative 4 power... Read More

Key Insights

• 🫵 Viewing negative exponents as reciprocals simplifies their computation.
• 🥡 The process involves taking the reciprocal of the base number and applying the positive exponent.
• ❎ Negative exponents can be applied to whole numbers and fractions.
• ❎ Negative numbers can also have negative exponents.

Questions & Answers

Q: How can negative exponents be interpreted?

Negative exponents can be interpreted as reciprocals. They indicate that the base number should be inverted and the positive exponent applied.

Q: What is 2 to the negative 4 power?

2 to the negative 4 power can be viewed as the reciprocal of 2 to the fourth power or, in other words, 1 divided by 2 to the fourth power, which equals 1/16.

Q: How does the negative exponent affect fractions?

When dealing with fractions, negative exponents can be resolved by finding the reciprocal of the fraction and applying the positive exponent. For example, 5/8 to the negative 2 power is equal to 64/25.

Q: Can negative numbers have negative exponents?

Yes, negative numbers can have negative exponents. The process remains the same—taking the reciprocal and applying the positive exponent. For example, -4 to the negative 3 power is equal to -1/8.

Summary & Key Takeaways

• The video explains how to compute negative exponents by viewing them as reciprocals.

• By using the concept of reciprocals, negative exponents can be rewritten as positive exponents.

• Examples of negative exponents with whole numbers and fractions are provided to illustrate the concept.