Simplest form for 2(2/3) + 3(2^(2/3))

[FMMurphy]

I am trying to put 2(2/3) + 3(2^(2/3)) in the simplest form. Could you please help me?

 

[stapel]

You've got a rational term and a term containing a cube root. I don't see that there is anything you can do to "simplify" this. You might restate it (using "cbrt()" instead of "to the one-third power") or rearrange it, but I don't see it "simplifying" at all.

Eliz.

 

[jwpaine]

I am trying to put 2(2/3) + 3(2^(2/3)) in the simplest form. Could you please help me?

Only thing I see possible is multiplying the 2(2/3) down to (2/3)(2/1) = (4/3)

Or, as stated above, restate your 3(2^(2/3)) with a radical as:

3(2^2)^(1/3) = 3*cbrt(4)

So, in the end, you would end up with (4/3) + 3 * cbrt(4)

I believe that is how you would do it. :?

 

[stapel]

That's all I could come up with, which is a restatement, using radicals, of the original expression. (Okay, we multiplied the 2 and the 2/3, but otherwise, we really didn't "simplify".)

If they're wanting anything else, I can't guess what it would be.

Eliz.

 

[FMMurphy]

Actually thr problem is 2^(2/3/) +[3 ]2^(2/3)

 

[axrw]

I tend to be pretty bad at math, but I believe that would simplify to 4[2^(2/3)].

It's like collecting like terms. They have the same base and exponent so you can add them.

 

[Denis]

Correct, axrw.
Murph, please take time to LOOK at your typing before hitting the send button :shock:

 

[stapel]

Actually thr problem is 2^(2/3/) +[3 ]2^(2/3)

What is the meaning of the second "slash" in the first fraction? What is the meaning of the brackets in the second term?

Thank you.

Eliz.

 

[soroban]

Hello, FMMurphy!

\(\displaystyle \text{Simplify: }\L\:2^{\frac{2}{3}}\,+\,3\cdot2^{\frac{2}{3}}\)

\(\displaystyle \text{We have: }\L\:4\cdot2^{\frac{2}{3}} \;=\;2^2\cdot2^{\frac{2}{3}} \;=\;2^{\frac{8}{3}}\)

 

[FMMurphy]

You have the problem right but where did you get the 4*2^(2/3) ? I understand from that how you got 2^(8/3) but I don't see where the 4 came from. Sorry for the misunderstanding in the problem. I'm just learning how to type these things!

 

[pka]

where did you get the 4*2^(2/3) ? I understand from that how you got 2^(8/3) but I don't see where the 4 came from.

One apple plus three apples equals four apples.
It is just that simple.

Here an apple is \(\displaystyle 2^{\frac{2}{3}}\).