How do you work out the value of ..

8 ^-2/3
(indices and powers)
the answer is 1/4

please explain it... thankyou

OK some basic rules for indices..

We all know what x^2 means but
x^(1/2) (x to the power a half) means the square root of x
x^(1/3) means the cube root of x etc

x^-1 means 1/x^1
x^-2 is 1/x^2 (one over x squared)


So working out your answer.... 8^-2/3

Negative index so 1/ 8^(2/3)
2/3 is just 2 times one third
x^1/3 is cube root of 8 = 2
Raise that to the power 2 to get 4
So answer is 1/4 or 0.25

Just take each part of the index and work on that. Its really much easier to be able to write things on 'normal mode' rather then on a computer!!!

8^-2/3
=1/8^(2/3)
=1/∛(8^2)
=1/∛(64)
=1/4 answer//

8^ -2/3 is the same as 1/ (b^2/3

8^2/3 = 64^1/3

64^1/3 = 4

So 8^-2/3 = 1/4

8^(-2/3) = (1/8)^(2/3) = (1/2)^2 = 1/4