Postby Technomancer » Thu Sep 29, 2005 6:38 pm
First, some notation: if you want to write "a to the power of b", write it as a^b. "a divided by b" should be a/b.
Anyways, the rule to remember is that when you divide exponentiated expressions of the same base, you subtract. If you're multiplying, you add. In your example b^12/b^4=b^(12-4).
The reason for this is relatively straightforward if you exand the exponent. For example:
b^3/b^4= (b*b*b)/(b*b*b*b).
Cancelling yields, 1/b=b^(-1)=b^(3-4).
The scientific method," Thomas Henry Huxley once wrote, "is nothing but the normal working of the human mind." That is to say, when the mind is working; that is to say further, when it is engaged in corrrecting its mistakes. Taking this point of view, we may conclude that science is not physics, biology, or chemistry—is not even a "subject"—but a moral imperative drawn from a larger narrative whose purpose is to give perspective, balance, and humility to learning.
Neil Postman
(The End of Education)
Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that my ignorance is just as good as your knowledge
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