Question

How do I change that from radical form to exponentisl expressionAnswer in the simplest form.

Answer 1

The radical form and exponential form are related by this:

`\sqrt[c]{b}^a=b^{(a)/(c)}`

So, applying this, we will have:

`\sqrt[]{9^3}=\sqrt[2]{9^3}=9^{(3)/(2)}`

However, we can simplify this, because:

`9=3^2`

So:

`9^{(3)/(2)}=(3^2)^{(3)/(2)}`

We can use the power to a power rule:

`(b^a)^c=b^(a\cdot c)`

So:

`(3^2)^{(3)/(2)}=3^{2\cdot(3)/(2)}=3^3`