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)`