Simplifying fractional indices

[umzung]

Homework Statement

How do we simplify to the given expression?

Relevant Equations

$$10π \left( \frac v {4π} \right)^{2/3} = 5\sqrt[3] {{V^2}\frac π 2}$$

$$10π \left( \frac V {4π} \right)^{2/3} = 5\sqrt[3] {{V^2}\frac π 2}$$Not sure how to deal with the $$10π$$ and how we get $$\frac π 2$$.

 

[Mark44]

$$10π \left( \frac V {4π} \right)^{2/3} = 5\sqrt[3] {{V^2}\frac π 2}$$

It took me a little while to understand what you're trying to do. At first I thought you were trying to solve the equation above. Then I realized that the goal was to simplify the expression on the left side, above.

Also, be more careful on the letters you use for variables. In your relevant equation, you have v (lower case) on one side and V (upper case) on the other. That was confusing as well.

Not sure how to deal with the $10π$ and how we get $\frac π 2$.

One thing to realize is that $(a)^{\frac 2 3}$ is equal to $(a^2)^{\frac 1 3}$. Can you start simplifying based on this hint?

 

[umzung]

I think I have it now.
The key to the answer is that $$10\pi=((10\pi)^{3/2})^{2/3}$$
which I can then bring inside the brackets.