Radical Notation with negative exponents, help needed.

[ochocki]

I understand these problems except for one thing, when the solution is not a real number.

For example

The problem (-4)^-3/2

I put the problem in a fraction to eliminate the negative exponent. Then, using the 2 in the index & the (-4)^3 as the radican I get 1/8 as my answer.

When I check my answer in the book it states "not a real number"

So here are my thoughts, please evaluate them and tell me if I am correct in my thinking:

When the radican is negative & the index is even the solution is not a real number.

This seems to be the pattern i notice, please explain this to me.

I apologize if my explanation is vague, please let me know if I left something out.

 

[stapel]

You have the following expression:

. . . . .\(\displaystyle \L (-4)^{-\frac{3}{2}}\)

To eliminate the "minus" from the exponent, you moved the base to the other side of the fraction line:

. . . . .\(\displaystyle \L \frac{1}{(-4)^{\frac{3}{2}}}\)

Apply the cubing:

. . . . .\(\displaystyle \L \frac{1}{(-64)^{\frac{1}{2}}}\)

In radical terms, this is:

. . . . .\(\displaystyle \L \frac{1}{\sqrt{-64}}\)

This, of course, is not defined in the real numbers.

I have a feeling you neglected some parentheses, so the calculator interpreted the expression as:

. . . . .\(\displaystyle \L -(4)^{-\frac{3}{2}}\)

This does indeed simplify to your answer:

. . . . .\(\displaystyle \L -\left(\frac{1}{4^{\frac{3}{2}}}\right)\, =\, -\left(\frac{1}{\sqrt{64}}\right)\,= \,-\,\frac{1}{8}\)

Hope that helps a bit.

Eliz.

 

[ochocki]

I understand now, I initially was applying the sqaure root to the -4, which I overlooked the fact that the square root of -4 is not in the real numbers, Simple mistake. Thanks, Oh yeah, i'm new to these boards, how do I write out the equations like you did where I can actually show the signs instead of writhing them out in words?

 

[stapel]

...how do I write out the equations...instead of writhing them out in words?

Go to the very top of this page, and look in the "Forum Help" pull-down menu for the links regarding LaTeX. The articles will describe the basic commands.

You can also frequently "see" the commands for a specific line of formatted text by putting your mouse "arrow" over the expression (if you're using Internet Explorer). For instance, putting your mouse over the following expression:

. . . . .\(\displaystyle \L \frac{1}{\sqrt{-64}}\)

...should display something along these lines:

\L \frac{1}{\sqrt{-64}}

Hope that helps.

Eliz.