Monday, January 16, 2006


Today in class we learned how to work with negative bases. The negative base is similar to postive base in powers. The thing with negative bases that if the power has a negative infront of it. -22 the product would automatically be a negative. The answer isn't a postive for you people wondering why it is a negative. The reason is you are multiplying a negative number to a postive number which will turn it to a negative answer. (-2 x 2) = -4. If your working with exponents like 99,5,63. The product will always be a negative. You always have to multiply with a negative number first than a postive number. Example: (-2 x 2 x 2 x 2...)

The other way with negative bases you might get a question like example (-2)2. The way you do this question is that you multiply with the same value with a postive or negative number value. So to do this question it is (-2 x -2) = 4. Remember if the exponent is an even number it will be a postive answer. If the exponent is an odd number it will be a negative answer.

A helpful hint: The exponent is only applied to what is directly in front of it.
Example: -54 means that the exponent is only for the 5 NOT the negative. In expanded form it would be -1 x 5 x 5 x 5 x 5 = -625
Example: (-5)4 means that the exponent is applied to the entire contents of the bracket. In expanded form it would be -5 x -5 x -5 x -5 = +625

We also learned to divide powers. Diving powers is pretty straight forward. If you have the same base with different exponents you just subtract the exponents and keep the same base number. Example: (23 รท -22) you keep the base which is 2 and you just subtract 3 - 2 which equals to 1. The final answer is 21


Powers with Negative Base Tips:

Just remember if you get a question like....

22 in expanded form: 2 x 2

-22 in expanded form: -2 x 2

(-2)2 in expanded form: -2 x -2

-(2)2 in expanded form: -1 x 2 x 2

-(-2)2 in expanded form: -1 x -2 x -2


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