The first step to solving this problem is to calculate the cube root. The first step to calculating this is to take the root of the fraction and then take the root of both the numerator and denominator separately. This will look like the following:
![\frac{ \sqrt[3]{-64} }{ \sqrt[3]{125} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%5B3%5D%7B-64%7D%20%7D%7B%20%5Csqrt%5B3%5D%7B125%7D%20%7D%20)
An odd root of a negative radicand is always negative,, so the top of the fraction will need to change to the following:
![\frac{- \sqrt[3]{64} }{ \sqrt[3]{125} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B-%20%5Csqrt%5B3%5D%7B64%7D%20%7D%7B%20%5Csqrt%5B3%5D%7B125%7D%20%7D%20)
For the bottom fraction,, you must write it in exponential form.
![\frac{- \sqrt[3]{64} }{ \sqrt[3]{ 5^{3} } }](https://tex.z-dn.net/?f=%5Cfrac%7B-%20%5Csqrt%5B3%5D%7B64%7D%20%7D%7B%20%5Csqrt%5B3%5D%7B%205%5E%7B3%7D%20%7D%20%7D%20)
Now write the top expression in exponential form
![\frac{- \sqrt[3]{ 4^{3} } }{ \sqrt[3]{ 5^{3} } }](https://tex.z-dn.net/?f=%20%5Cfrac%7B-%20%5Csqrt%5B3%5D%7B%204%5E%7B3%7D%20%7D%20%7D%7B%20%5Csqrt%5B3%5D%7B%205%5E%7B3%7D%20%7D%20%7D%20)
For the bottom of the fraction,, reduce the index of the radical and exponent with 3.
![\frac{ - \sqrt[3]{ 4^{3} } }{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%20%5Csqrt%5B3%5D%7B%204%5E%7B3%7D%20%7D%20%7D%7B5%7D%20)
Now reduce the index of the radical and exponent with 3 on the top of the fraction.
Lastly,, use
to rewrite the fraction.
This means that the correct answer to this question is option A.
Let me know if you have any further questions
:)
An odd root of a negative radicand is always negative,, so the top of the fraction will need to change to the following:
For the bottom fraction,, you must write it in exponential form.
Now write the top expression in exponential form
For the bottom of the fraction,, reduce the index of the radical and exponent with 3.
Now reduce the index of the radical and exponent with 3 on the top of the fraction.
Lastly,, use
This means that the correct answer to this question is option A.
Let me know if you have any further questions
:)
