64to the power of -2/3?

64^-⅔ = (64^⅓)ˉ² = (∛64)ˉ² = 4ˉ² = 1/(4²) = 1/16

you can separate the -2/3 into three parts

(-1)(1/3)(2)

because of exponent laws you can now apply them separately

easiest to start with the 1/3. Take the cube root of 64, which is 4 (4^3 = 64)

so now we have (4^2)^-1 = 1/16

64=2^6
64^(-2/3)=2^(6*-2/3)=2^-4=1/16

64^(-2/3)
=1/[64^(2/3)]
=1/[(4^3)^(2/3)]
=1/(4^2)
=1/16

64 ^ -2/3= 4 ^-2=4^ 1/2=1/16

Ok first of all the minus in the power just means one over, so basically the answer is going to be 1/(64^2/3)

When you have a fraction as a power what it means is bring the number to the power that is on the top of the fraction and take the nth root, where n is the number on the bottom. These can be done in any order.

So in this example we want to square 64 and take the cubic root. In my opinion it will be easier to take the cubic root first in this situation because trying to find the cubic root of a huge number like 64^2 would be hard.

Therefore first of all take the cubic root of 64, which is 4 and square it to give 16.

Then we just need to put one over this answer and therefore our final answer is 1/16.

64^(- 2/3) = 1 / 64^(2/3) = 1 / 4² = 1 / 16

PS
Don't say that you are dumb-------never give in !

64^(-2/3)
= ³√(64^-2)
= ³√[(4^3)^-2]
= ³√[(4^-2)^3]
= 4^-2
= 1/4^2
= 1/16