simplify the radical. assume that all variables represent positive real numbers. \n\nselect the correct…
simplify the radical. assume that all variables represent positive real numbers. \n\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice. \n\na. \n\nb. the radical does not represent a real number.
Answer
Explanation:
Step1: Factor the radicand
$$ \sqrt[3]{-27x^{9}y^{12}}=\sqrt[3]{(-3)^3\cdot(x^{3})^3\cdot(y^{4})^3} $$
Step2: Apply the cube - root property $\sqrt[3]{a^3}=a$
$$ \sqrt[3]{(-3)^3\cdot(x^{3})^3\cdot(y^{4})^3}=-3x^{3}y^{4} $$
Answer:
A. $\sqrt[3]{-27x^{9}y^{12}}=-3x^{3}y^{4}$