Question

Cube root of - 1000p^12q^3

Answer 1

$\bf \sqrt[3]{-1000p^{12}q^3}~~ \begin{cases} 1000=10^3\\ (-1)^3=-1\cdot -1\cdot -1\\ \qquad -1\\ p^{12}=p^{4\cdot 3}\\ \qquad (p^4)^3 \end{cases}\implies \sqrt[3]{(-1)^3(10)^3(p^4)^3q^3} \\\\\\ (-1)(10)p^4q\implies -10p^4q$