How Do You Simplify the Expression 1/3π(2h/3)^2 * h into 4π/27 * h^3?

[nukeman]

Simple question: 1/3pi(2h/3)^2 * h ?

Homework Statement

Can someone please refresh me on the steps:

1/3∏(2h/3)^2 * h

HOW does that turn into:

4∏/27 * h^3

?

Homework Equations

The Attempt at a Solution

 

[SammyS]

Homework Statement

Can someone please refresh me on the steps:

1/3∏(2h/3)^2 * h

HOW does that turn into:

4∏/27 * h^3
?

Homework Equations

The Attempt at a Solution

What is (2h/3)² ?

 

[nukeman]

4h/9

 

[SammyS]

4h/9

Why didn't you square the h ?

 

[NascentOxygen]

Homework Statement

Can someone please refresh me on the steps:

1/3∏(2h/3)^2 * h

There is a lazy convention which unfortunately has been granted some legitimacy, where some people interpret your line of text to be something different to how most see it.

In your problem, since we know the answer we are working towards, we can work backwards to reveal what is intended, then proceed forwards and solve it.

To leave no doubt in anyone's mind, it is recommended that you be generous with the use of parentheses when forming expressions in text, e.g. write it as (1/3)∏(2h/3)^2 * h when that is what is intended.

Or, if you can find a genuine fraction character, you can use it to eliminate ambiguity, e.g., ⅓∏(2h/3)^2 * h

I have labored the point simply because some people interpret 1/3∏(2h/3)^2 to have an equivalence with
1/(3∏(2h/3)^2), but for your question such an interpretation does not lead to the given answer (so that is the only evidence we have that it is not the interpretation intended here).