Question

What is the cube root of 27a^l2?
-3a4
-3a
3a
3a*​

Answer 1

`3a^4`

Explanation:

What is the cube root of
`27a^(12)`? This is the question.

We can write:

`\sqrt[3]{27a^(12)}`

We will use the below property to simplify:

`\sqrt[n]{a*b}=\sqrt[n]{a}  \sqrt[n]{b}`

So, we have:

`\sqrt[3]{27a^(12)} =\sqrt[3]{27} \sqrt[3]{a^(12)}`

We will now use below property to further simplify:

`\sqrt[n]{x} =x^{(1)/(n)}`

Thus, we have:

`\sqrt[3]{27} \sqrt[3]{a^(12)} =3*(a^(12))^{(1)/(3)}`

We know power to the power rule:
`(a^z)^b=a^(zb)`

Now, we have:

`3*(a^(12))^{(1)/(3)}\\=3*a^{(12)/(3)}\\=3a^4`

This is the correct answer:
`3a^4`