Answer:
Because the cubed root of the numerator and denominator equals the answer
Step-by-step explanation:
alright, we are trying to understand WHY [tex]\sqrt[3]{\frac{-8}{27} } = -\frac{2}{3}[/tex]
You can actually rewrite the first number as [tex]-\frac{\sqrt[3]{8} }{\sqrt[3]{27} }[/tex]
you must look for the number, which three times itself, equals 8...
...and the same thing for the bottom: a number, which three times itself... equals 27.
What number cubed equals 8? The answer is 2
What number cubed equals 27? The answer is 3
...so now we have -2 over 3. You can double check this answer.
[tex]-\frac{2}{3} * -\frac{2}{3} = \frac{4}{9}[/tex]
[tex]\frac{4}{9} * -\frac{2}{3} = -\frac{8}{27}[/tex]
we get the original number that we were looking for the cubed root... SUCCESS.
