Question

How do i show that this equation equals this?

Answer 1

Answer:

See explanation below.

Step-by-step explanation:

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

$\sqrt[x]{b^{m}}=(b^{m})^{\frac{1}{x}}=b^{m*\frac{1}{x}}=b^{\frac{m}{x}}$

$(\sqrt[x]{b})^{m}=(b^{\frac{1}{x}})^{m}=b^{m*\frac{1}{x}}=b^{\frac{m}{x}}$

So we have shown that:

$\sqrt[x]{b^{m}}=b^{\frac{m}{x}}$

and

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

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