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### Course: Class 7>Unit 5

Lesson 4: Negative exponents

# Negative exponent intuition

How do negative exponents work? Let's build our intuition about why a^(-b) = 1/(a^b) and how this definition keeps exponent rules consistent. Continue the pattern of decreasing exponents by dividing by 'a', and see how it extends to zero and negative powers. While we're at it, we'll see why a^0 =1. Created by Sal Khan.

## Want to join the conversation?

• What is understanding exponents useful for? can it ever be used in daily life?
• You can use them for taxes, material management, and funds.
• Why do we even use exponents; when will we ever even use them in life?
• Here are some real life applications of exponents.

1. Calculations of areas (including surface areas) and volumes of objects
2. Calculations of distances in situations involving right triangles (Pythagorean Theorem)
3. Calculations involving loans or savings accounts, when interest is compounded
4. Calculations of probabilities of compound events
5. Calculations pertaining to motions of objects (for example, the height of an object thrown in the air as a function of time)
6. Expressing very small or very large measurements in science (for example, using scientific notation to express the mass of an electron or the mass of a planet)
7. Geometric Brownian motion model of the behavior of stock prices
8. Calculations in statistics, such as variance and standard deviation
9. Population growth or decay models

Have a blessed, wonderful day!
• I wonder if Sal ever looks at the comments
• Could somebody explain going backwards with exponents? It's a little bit difficult to understand.
• Think of this pattern:
2^3=8
2^2=4
2^1=2
2^0=1
2^-1=1/2
2^-2=1/4

See how we have a pattern of dividing by two every time? So going down in exponents equates to dividing instead of multiplying!
• does anybody know what a and b are??
• a and b are variables that stand for any number.
• what is 0 to the 0th power
• it is undefined, since x^y as a function of 2 variables is not continuous at the origin
• Potato Quality XDD I understand this video is ancient.
• I love knowing the WHY of these conventions, makes everything in math feel so much more solid, symmetrical and wonderful
• what is 0 to the 0th power