-3 * (a)^(-1) = -3/a

Let a = -2

-3 * (-2)^(-1) = -3/(-2) = +3/2

Solved

Posted on 2011-04-18

This is the question and the answer, but I don't understand it.

With an exponent of ^2 it's a simple matter -3(-2)^2 = -3(4). But the problem below has both a negative exponent and an exponent less than 2. Can someone help me understand first how a negative exponent effects a problem and then how an exponent of less than 2 effects a problem? Thanks.

-3(-2)^-1 = -(3/-2)

With an exponent of ^2 it's a simple matter -3(-2)^2 = -3(4). But the problem below has both a negative exponent and an exponent less than 2. Can someone help me understand first how a negative exponent effects a problem and then how an exponent of less than 2 effects a problem? Thanks.

-3(-2)^-1 = -(3/-2)

6 Comments

So, if a = -2, then a^(-2) = 1/( a^2 ) = 1/( (-2)^2 ) = 1/( -2*-2 ) = +1/4

Consider a^5/a^3 = (aaaaa)/aaa = aa = a^2

which leads to a natural formula to remember:

Now consider a^3/a^5 = aaa/(aaaaa) = 1/(aa) = 1/a^2

But, if you try to use the above formula, you get a^3/a^5 = a^(3-5) = a^(-2)

So, someone said, let's define a negative exponent to be:

and since this one formula seemed to fit well into algebra, it stuck.

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