Question

How do i show that this equation equals this?

Answer 1

See explanation below.

Explanation:

So we will have to somehow show that
`\sqrt[x]{b^(m)}` equals
`(\sqrt[x]{b})^(m)` by using
`b^{(m)/(n)}`.

`\sqrt[x]{b^(m)}=(b^(m))^{(1)/(x)}=b^{m*(1)/(x)}=b^{(m)/(x)}`

`(\sqrt[x]{b})^(m)=(b^{(1)/(x)})^(m)=b^{m*(1)/(x)}=b^{(m)/(x)}`

So we have shown that:

`\sqrt[x]{b^(m)}=b^{(m)/(x)}`

and

`(\sqrt[x]{b})^(m)=b^{(m)/(x)}`

So by the transitive property of equality:

`\sqrt[x]{b^(m)}=(\sqrt[x]{b})^(m)`

I hope you find my answer and explanation to be helpful. Happy studying. :D