Question

What is the cube root of -1,000p^12q^3?

a)-10p^4
b)-10p^4q
c)10p^4
d)10p^4q

Answer 1

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

Answer 2

Its actually -10p^4q or b.