Work out the value of 27 ^-2/3

In order to answer this question we should first break it down into simpler parts.

Using the law of indices we can start this process.



Using the law above we can break down the components of the original question into two parts, “m” and “n”. In this case our “m” will be -2 and our “n” will be ⅓.



This means we can now rewrite our original question below.



With this simplified version we can start to answer the question.

First we solve 27^(⅓).

A fractional power means we root it to the nth power, with n being the denominator. In this case as our fraction is ⅓ our denominator is 3. Therefore, we take the cube root of 27 which gives us 3.



Lastly we solve for the negative power. With negative powers we take the number that is being raised and take 1 over it, then raising it to the positive value of the power.

That means our 3^-2 is going to 1/ (3^2). Doing this we are left with 1/9.



Therefore the final answer to the value of 27^-⅔ is 1/9.