Question

What is the cube root of 512m^12n^15?

Answer 1

Cube root of 512 = 8

of m^12 = m^(12/3) = m^4

of n^15 = n^5


Answer is 8m^4n^5

Answer 2

we have

$\sqrt[3]{512m^{12}n^{15}}$

we know that

$512=2^{9}$

substitute

$\sqrt[3]{2^{9}m^{12}n^{15}}=({2^{9}m^{12}n^{15}})^{(1/3)}\\=(2)^{(9/3)}m^{(12/3)}n^{(15/3)} \\= 2^{3} m^{4} n^{5} \\= 8m^{4}n^{5}$

therefore

the answer is

$8m^{4}n^{5}$