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I hope this question is not that stupid.

$y=x^{\frac{-2}{3}}$ is $y=\frac{1}{\sqrt[3]{x^{2}}} $right? But when I type $y=x^{\frac{-2}{3}} $and $y=\frac{1}{\sqrt[3]{x^{2}}}$into Mac Grapher,I got different pictures.

Since my reputation is not over 10,I can't post them,but it's very easy to do that.$y=x^{\frac{-2}{3}}$ did not show on negative direction of X-axis,while $y=\frac{1}{\sqrt[3]{x^{2}}}$ showed on all X-axis.

EDIT:Thank you everyone,I can post pictures now enter image description here enter image description here

or more examples

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and in some case they are same

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Here are some polynomial examples. Ther're also equal enter image description here enter image description here

Another set enter image description here enter image description here

And I did some research ,you can see Mac Grapher only show function with integer exponents enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here enter image description here

Change 3 to 5 enter image description here enter image description here enter image description here enter image description here enter image description here

I could go on,but you get the ideas.

Why did this happen,is there something wrong with my precalculus skill or Mac Grapher?

Update:Some guy in Apple forum said"The functions are not the same. In the first case, you're raising a real number to a fractional power. That's ambiguous for negative arguments, so the program only graphs it for non-negative arguments. In the second case, you're raising a non-negative number to a fractional power."

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    Hello, I think you are graphing wrong function if your question is correct. it should be $y=x^{\frac{-2}{3}}$ and not $y=x^{\frac{2}{3}}$2012-11-28
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    In fact, Grapher assumes the domain of $x^{1/3}x^{1/3}$ is all real numbers, but not $x^{2/3}$.2012-11-28
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    @PaulDirac I think in between posting his question and his pictures, OP recognized that Grapher has this odd feature whether or not the exponent is negative.2012-11-28
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    @countinghaus yes you're right, I just thought I would point it out. I don't think there's something wrong about your Grapher, I plotted same two functions on Mathematica, and got same results, but I don't know why.2012-11-28
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    @Paul Dirac Hello,thanks for the help,pictures edited now!2012-11-28
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    I used by trusty TI-83 calculator and it graphed all of the functions over the whole domain with no problems.2012-11-29
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    @ so it's not my precalculus skill,right?Good Lord,I have checked those functions for almost 2 hours...Is this a bug in Mac Grapher then?I will keep this post updated,and draw some graph in other software.2012-11-29

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