Definitions:
- NEGATIVE EXPONENTS : THE NEGATIVE EXPONENT STATES HOW MANY TIMES IT IS DIVISIBLE BY THE NUMBER
- QUOTIENT RULE: THE QUOTIENT RULE STATES THAT WE CAN DIVIDE TWO POWERS WITH THAT WE CAN DIVIDE TWO POWERS WITH THE SAME BASE BY SUBTRACTING THE EXPONENTS.
Sample Problems
A negative exponent means how many times to divide by the number.
Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125
Or many divides:
Example: 5-3 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008
So, what about 8-2 ?
Example: 8-2 = 1 ÷ 8 ÷ 8 = 1/82 = 1/64 = 0.015625
Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125
Or many divides:
Example: 5-3 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008
So, what about 8-2 ?
Example: 8-2 = 1 ÷ 8 ÷ 8 = 1/82 = 1/64 = 0.015625
![Picture](/uploads/4/4/3/2/44329011/2520623.gif?250)
In the sample problem you see how you have to divide the coefficients (which in this picture they have made a mistake due to 4/4 being 1) of the numerator by the denominator and then subtract thee exponents in this case being 5 in the numerator and 2 in the denominator.
Explanation:
When dealing with negative exponents you do NOT multiply as you would for when you get a positive exponent. Instead you will do the complete opposite and divide when a negative exponent is present. For example if the problem says 3 to the power of negative 4 , you will end up with a solution of 1/3 to the fourth power. due to the exponent being negative you will put 1 over 3 to get the negative exponent to turn into a positive exponent. When dealing with the quotient rule you will need to divide the numerator by the denominator. When you have completed that step you will then subtract the exponents. If the exponent in the denominator is greater than the exponent in the numerator you will have to move the exponent to the denominator instead of leaving the exponent in the numerator. |
Similarities: In both these situations you divide in some sort of way and you are looking for a solution.
Differences: When dealing with negative exponents you you do not need to divide a coefficient by a coefficient you just divide the number by the times the exponent states to do so and when dealing with the quotient rule you divide coefficient by coefficient and you also subtract the exponents something you do not do when dealing with negative exponents. |
Real-World Examples:
|
Sources
Definitions: http://www.math.com/school/subject2/lessons/S2U2L2DP.html
http://www.mathsisfun.com/algebra/negative-exponents.html
Sample Problems: http://www.math.com/school/subject2/lessons/S2U2L2DP.html
http://www.mathsisfun.com/algebra/negative-exponents.html
Real-world Examples: http://passyworldofmathematics.com/exponents-in-the-real-world/
_
Definitions: http://www.math.com/school/subject2/lessons/S2U2L2DP.html
http://www.mathsisfun.com/algebra/negative-exponents.html
Sample Problems: http://www.math.com/school/subject2/lessons/S2U2L2DP.html
http://www.mathsisfun.com/algebra/negative-exponents.html
Real-world Examples: http://passyworldofmathematics.com/exponents-in-the-real-world/
_