- Thread starter Quasimoto
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1st expression = ~.5443Dear forum users,

I've been trying to figure this out.

View attachment 12584

Could someone explain to me how this is the answer?

View attachment 12585

Thank you in advance!

2nd expression = ~2.0528

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As noted by the expansion that tkhunny is using the "solution" given in the OP is incorrect. The actual answer has a \(\displaystyle \sqrt{2}\) in the denominator. The fraction in front of the radicals is wrong as well.1st expression = ~.5443

2nd expression = ~2.0528

Is this the solution to a different problem?

-Dan

I am following it yes.

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I looked for the answer again and yes the solution is to a different problem.As noted by the expansion that tkhunny is using the "solution" given in the OP is incorrect. The actual answer has a \(\displaystyle \sqrt{2}\) in the denominator. The fraction in front of the radicals is wrong as well.

Is this the solution to a different problem?

-Dan

But my original answer is still wrong.

So I will be trying to figure it out later today.

Thank you

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You posted two images:Dear forum users, I've been trying to figure this out.

\(\displaystyle \boxed{\left(\dfrac{2\sqrt3}{3\sqrt2}\right)^3}\) & \(\displaystyle \boxed{\frac{32}{27}\sqrt3}\)

The second image

You tell us at what step you fail to understand.

1) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{2\sqrt3\cdot\sqrt2}{3\sqrt2\cdot\sqrt2}\)

2) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{2\sqrt6}{3\cdot 2}\)

3) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{\sqrt6}{3}\)

4) \(\displaystyle \left(\frac{\sqrt6}{3}\right)^3=\frac{6\sqrt6}{27}\)

5) \(\displaystyle \boxed{\left(\frac{\sqrt6}{3}\right)^3=\frac{2\sqrt6}{9}}\) CLICK HERE

The second image is indeed the wrong solution to the problem.You posted two images:

\(\displaystyle \boxed{\left(\dfrac{2\sqrt3}{3\sqrt2}\right)^3}\) & \(\displaystyle \boxed{\frac{32}{27}\sqrt3}\)

The second imageis notthe reduction of the first.

You tell us at what step you fail to understand.

1) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{2\sqrt3\cdot\sqrt2}{3\sqrt2\cdot\sqrt2}\)

2) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{2\sqrt6}{3\cdot 2}\)

3) \(\displaystyle \frac{2\sqrt3}{3\sqrt2}=\frac{\sqrt6}{3}\)

4) \(\displaystyle \left(\frac{\sqrt6}{3}\right)^3=\frac{6\sqrt6}{27}\)

5) \(\displaystyle \boxed{\left(\frac{\sqrt6}{3}\right)^3=\frac{2\sqrt6}{9}}\) CLICK HERE

Thank you for explaining step by step.

I failed at step 4, I used the exponent at the beginning instead of solving everything what is inside of the parentheses.

Thank you very much I appreciate the time and effort.