# Lesson 1: Zero and Negative Exponents

## Lesson 1: Zero and Negative Exponents

• Main point 1: As we know from our previous lessons, mathematicians have a convention for expressing a number multiplied by itself (called exponents), where x is a shorthand notation for saying “x is multiplied by itself by a times”.
• Main point 2: Zero and negative exponents follow the same pattern that positive exponents follow. Just as we multiply the number again to increase the exponent (x -> x ), we divide by the number to reduce the exponent (x ->x )
• Main point 3: Mathematicians have agreed that x =1, because it’s consistent with the pattern: x = x /x = x/x = 1
• Main point 4: When we continue this process into the negative integers, we find that x   = x /x = 1/x. Likewise we can express the rule as a general formula: x  =1/x
• Main point 5: You can simplify expressions by changing a negative exponent into the inverse, write out the exponent and apply standard arithmetic rules.
• Main point 6: inverse of an inverse is the number itself 1/1/x=x
• Main point 7: multiplication of an inverse applies to the result: 2/1/x=2*(1/1/x)=2x