(64x-³)-²/³ <--- Why is the answer: x²/16 ?? Please help me

[ElectroNewby]

I need to solution: (64x-³)-²/³.

Why is the answer: x²/16 ?

Please help me
Thanks. Everything was fine in my mathbook until I came across that one.
(+sorry for the bad use of english)

 

[MrAl]

Hello,

What you do is try to separate parts so you can do it a little at a time.

One way to do this is to first break up the problem into:
64^(-2/3)*(x^(-3))^(-2/3)

Now the first part is:
64^(-2/3)

which equals:
(1/64)^(2/3)

and the second part is:
(x^(-3))^(-2/3)

which equals:
(x^3)^(2/3)

So the first part:
(1/64)^(2/3)

is the same as:
1/(64^(2/3))

and the 2/3 means take the third root and then square it, so we get:
1/(4)^2

which equals:
1/16

and the second part:
(x^(-3))^(-2/3)

is the same as:
(x^3)^(2/3)

which means take the third root of x^3 and then square it, so we get:
x^2

Now multiplying these two new parts back together we get:
(1/16)*x^2

or rewritten:
x^2/16

which is the answer.

 

[ElectroNewby]

Hello,

What you do is try to separate parts so you can do it a little at a time.

One way to do this is to first break up the problem into:
64^(-2/3)*(x^(-3))^(-2/3)

Now the first part is:
64^(-2/3)

which equals:
(1/64)^(2/3)

and the second part is:
(x^(-3))^(-2/3)

which equals:
(x^3)^(2/3)

So the first part:
(1/64)^(2/3)

is the same as:
1/(64^(2/3))

and the 2/3 means take the third root and then square it, so we get:
1/(4)^2

which equals:
1/16

and the second part:
(x^(-3))^(-2/3)

is the same as:
(x^3)^(2/3)

which means take the third root of x^3 and then square it, so we get:
x^2

Now multiplying these two new parts back together we get:
(1/16)*x^2

or rewritten:
x^2/16

which is the answer.

Hey thank you so much for helping.

Altough I found another way of getting the answer:

(64x-³)-²/³

64^-2/3 = 0.0625
x^(-3 times -2/3) = x2

So I ended up with: 0.0625 x^2

0.0625/1 = 1/-0.0625 = -16

So -16x^2

So x^2/16

It was actually pretty simple... but this stuff is so far away from me... I did maths like 7 yrs ago :S

Thanks a lot !!

 

[MrAl]

Hello again,

Sounds like you found another way to do it and that's good too. I guess you have this problem solved now.

 

[OutToLunch]

i would suggest staying away from the calculator as much as possible. most of the problems in text books will be fairly clean and knowing the cube root of 64 (and other similar operations) or knowing how to obtain it without a calculator is a valuable skill.

 

[ElectroNewby]

How do you want me to know what is 64^-2/3 without a calculator ???

Come on... I know the cubic root of 64, but if I see 64^-2/3 in my head it translates as "wtf".

When I see 64^-2/3, I don't have the skills to say that that that and that bang cubic root (still don'T understand where you see cubic root) and further more, in this problem I don't know where the cubic root of 64 is.

I did not deal with the number 4. (?)

 

[dknguyen]

You just gotta get used to the fact that the x-root of y can also be written as y^(1/x) or y^(x^-1).

like the sqrt(y) = y^(1/2) = y^0.5
or cubed root of y = y^(1/3) = y^0.33...

The reason you can't see the cubed root is because of the poor unbracketed way you typed out your expression. You typed

(64x-³)-²/³

To be honest I had no idea what you actually meant when you typed that out in your first post. You really need to use brackets or a superscripted divide sign (which we dont have on this forum as far as I know)

And just now you typed it out as:
64^-2/3

which actually means
(64^-2)/3

What you should have typed:

64^(-2/3)

That's the same as
[ 64^(1/3) ]^-2

THe underlined part is your cubed root right there. And working with digital circuits or programming gets you really used to numbers that are powers of 2 like 8, 16, 32, 64, or 128 so you get a really good feel for those numbers. I don't know what the cube root of 64 offhand is either but I do have a good feeling there is a cubed root to it just from getting used to seeing how those powers of 2 numbers fit together after working with them a bit. You don't realy need the cubed root of 64 memorized either since if you can break the expression down you can see that there's a cube root of 64 in there and then you can just punch that into the calculator. It's rather odd if you break it down and end up isolating the cubed root of 64 and say "I can't simplify it anymore so I'll just leave it as it is."

Like for 64 if I see a cube root of 64 somewhere, from just being used to the way the powers of 2 numbers fit together I get a good feeling it's going to be an integer answer. From there you can just hunt it down with multiplication or powers in your head. You should be able to do 2^3 all the way up to maybe 5^3 in your head which lets you hunt down which one is equal to 64.

You don't need them memorized either. Just break down the multiplcations down to simple steps in your head (for me it's usually breaking it down to simple multiplications and adding everything up afterwards, I don't think about it like how you would do multiplication on paper). Like for 5^3 I go 5^2 = 25. Now what is 25*5? I don't multiply 25*5 since I suck at doing "multiplication on paper and carrying the 1 in my headso much as I go "I know 25*4 = 100 and I'll just add on another 25 so that's 125.

I wouldn't worry about working on it. It just comes in time.