Question

What is the cube root of 512m12n15
Could anyone plz help me?

Answer 1

C. 8m^4n^5[/tex]

Explanation:

We are given
`\sqrt[3]{512m^(12)n^(15)  }`

The cube root is nothing but the power of
`(1)/(3)`

Now we have to write 512 as the power 3.

512 = 8.8.8 =
`8^(3)`

So,
`\sqrt[3]{512m^(12)n^(15)  }` =
`(8^(3).m^(12).n^(15))   ^{(1)/(3)}`

We know that the exponent property:
`(a^(m) )^n= a^(mn)`

Using this property, we can simplify the exponents.

=
`8.m^(4) .n^5 = 8m^4n^5`

Answer 2

`8m^4n^5`

Explanation:

cube root is basically taking to the power of
`(1)/(3)`

Also, there is a property that is
`(x^m)^n=x^(mn)`

We can use these and find the cube root of the expression:

`(512m^(12)n^(15))^{(1)/(3)}\\=(512)^{(1)/(3)}*(m^(12))^{(1)/(3)}*(n^(15))^{(1)/(3)}\\=8*m^{(12)/(3)}*n^{(15)/(3)}\\=8*m^4 * n^5`

Thus, third answer chioce is right.