Answer:
[tex]\frac{1}{10c^{3}d^{4} }[/tex]
Step-by-step explanation:
THE GIVEN EXPRESSION IS
[tex]\sqrt[3]{\frac{1}{1000c^{9}d^{12} } }[/tex]
To simplify this expression, we just have to apply the cubic root to each part of the fraction, as follows
[tex]\frac{\sqrt[3]{1} }{\sqrt[3]{1000c^{9} d^{12} } }[/tex]
Then, we solve each root. Remember that to solve roots of powers, we just need to divide the exponent of the power by the index of the root, as follows
[tex]\frac{1}{10c^{\frac{9}{3} } d^{\frac{12}{3} } }[/tex]
Therefore, the equivalent expression is
[tex]\frac{1}{10c^{3}d^{4} }[/tex]
So, the right answer is the third choice.
