What is (2/3)^(-1/3)?

We can split this power into two bits - the negative sign and the fraction.

Let's deal with the negative sign first and forget about the fraction.

So a negative always means '1 over', or the fancy word for this is reciprocal. This just means that we flip the top and bottom number of our fraction over. Notice that when we have a whole number, an integer, this number is just over 1. So if we had (2)^-1/3, this would become (1/2)^1/3.

In our case then, the negative sign just flips over the 2 and 3 -> (3/2)^1/3.

Next look at the fraction in the power. With this, all we need to remember is 'root' - which is the root? The bottom is the root.

In other words, we take the bottom number of our fraction in the power and root our number to the appropriate degree. Here, with 3, we take the cube-root.

The top number works like a normal power - like a^2, we just get axa.

Combining this together, we have:

(3/2)^(1/3) = cube-root(3/2)^1 = cube root (3/2).

Now this looks horrible, but I promise that it's the answer.

Answered by Oliver R. Maths tutor

3293 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Aditi, Becky and Cali collect coins. Aditi has 6 more coins than Becky. Cali has 1 less coin than Aditi. Altogether they have 71 coins. How many coins do they each have? Show all your working.


How do you use the completing the square method to solve a quadratic equation?


Solve (x/4)-(2x/x+2)=1. Give your solutions to 2 decimal places.


There are 495 coins in a bottle. 1/3 of the coins are £1 coins. 124 of the coins are 50p coins. The rest of the coins are 20p coins. Work out the total value of the 495 coins


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences