Education for the 21st Century: Technology and Carbon Based Teaching/Training/Coaching and Mentoring

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