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
or more examples
and in some case they are same
Here are some polynomial examples. Ther're also equal
Another set
And I did some research ,you can see Mac Grapher only show function with integer exponents
Change 3 to 5
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."