Question

simplify the expression \\(\sqrt3{\frac{-64}{343}}\\).

select one:
a. \\(-\frac{64}{7}\\)
b. \\(-\frac{4}{343}\\)
c. \\(-\frac{4}{7}\\)
d. \\(\frac{4}{7}\\)

Explanation:

Step1: Split root into numerator/denominator

$$\sqrt[3]{\frac{-64}{343}} = \frac{\sqrt[3]{-64}}{\sqrt[3]{343}}$$

Step2: Evaluate cube roots

$\sqrt[3]{-64} = -4$ since $(-4)^3=-64$; $\sqrt[3]{343}=7$ since $7^3=343$

Step3: Combine results

$$\frac{-4}{7} = -\frac{4}{7}$$

Answer:

C. $-\frac{4}{7}$