Easy math problem...?

Question

ok now i feel reaaaaaally stupid in asking this but summer just ended so hey! give me a break! ok. so so i know 64^(2/3) is 16. but how do you get there by hand? w/o calculator.

Answer 1

(1) 64 = 8*8 = (2^3)*(2^3)

(2) 64^(1/3) = [(2^3)*(2^3)]^(1/3) = 2^2

(3) 64^(2/3) = (2^2)^2 = 4^2 = 16

Answer 2

the exponent (2/3) means two things:  the number is going to be squared and also the cube root will be taken.

You can do either step first, but with out a calculator you probably don't want to do 64 squared.  So start with the cube root.

The cube root of 64 is 4.  Then square this number

4 squared is 16

Answer 3

64^(2/3)=denominator rt (64^2)    (rt is root)  So,

64^2=4096  (2 is the numerator of the fraction)

3rt(4096)= 16  (3rt is also cube root)

To do this all by hand, you need to multiply 64 by 64.  You kinda need to experiment or know that 16^3 is 4096, but it shouldn't take long to find out.  If you know how, you can base it off 64 sometimes.

Hope this helped!

Answer 4

64^(2/3) = 64^(2 x 1/3)

1) take the cube root of 64, i.e. 64^(1/3)

2) square that

When you see 64 and 16... you should be able to make a good guess of what numbers are involved.  HINT: 64 and 16 are both even.

OR

work backwards, meaning instead of

64^(2 x 1/3)

do

16^(3/2) = 16^(3 x 1/2)

16^(1/2) = ?

?^3 = 6?

Answer 5

You have to do 64^2 first, then take the cube root of that answer.

It's the same thing with square roots but you just don't think of it that way.  16^(1/2) is the same as the sqrt(16) which we know is 4.  So you do 16^(1), then square root it.  Same thing.  That's how I remember the order when you have a fractional exponent.  Just do something with a square root that you know the answer to, to make sure you've got the order right.

Answer 6

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Answer 7

you will do 64 squared (2) and then cube root (3) that to get you 16  

Answer 8

alright, I know a whole bunch of other people did this, but my way will probably benefit you on all the other questions like this. so...

first break it up into a radical. so you get: radical 62 squared with the three above the radical symbol. (make sure when you have fractional exponents that the numerator is put as a power to the radicand and the denominator is the exponent of the radical) so in this case, your gonna square 64 to get 4096. so right now you got radical 4096 with a cubed root on the radical. so you need a number that will cubed perfectly into 4096. That number is 16, because 16*16*16=4096.

Answer 9

64 ^ (2/3) is really (64^2)^1/3 so break it down

cube root of 64 is 4

4 squared is 16.

Answer 10

start from the answer and work backwards.

EXAMPLE: x+2=4

^since you add 2 to x to get 4 you take it away to give you x

Try it on your problem! hope it helps =]

Answer 11

2/3 = 2 * 1/3

Do the cube root first, then the square