MYTUTOR SUBJECT ANSWERS

1162 views

Work out the value of 125 to the power of -2/3.

We want to find 125-2/3. To do this, we will need to use lots of power rules that we have learnt.

Firstly, when we put a power to another power, we multiply the two powers. For example, (23)4  (2 to the power of 3, ALL to the power of 4), is equal to 23x4 = 212.

We are going to use this rule in reverse. We can rewrite our power, -2/3, as the product of numbers that we know how to work with as powers.

Examples of powers that we know how to use, are:

Positive integers, such as 2 or 3: we just multiply the number by itself this many times, as usual. 
-1 : we put 'one over' the number. For example, 3-1 = 1/3.
Fractional powers, of the form 1/n : we take the n-th root. For example, 41/2 = square root of 4 = 2.

Firstly, we can factor out the negative to make things easier for ourselves, as we know how to work with -1 as a power. So, -2/3 = -1 x 2/3.

Secondly, we know how to use fractional powers, if they have a 1 in the numerator. So, 2/3 = 2 x 1/3.

Putting this all together, we have -2/3 = -1 * 2 * 1/3.

Back to our original question now!

We want to find 125-2/3 which we can now rewrite using our 'power of a power' rule in reverse, to get ((1251/3)2)-1. Because we can multiply numbers in any order and still get the same result, we can apply these powers in any order. But, some orders are often easier than others. I like to do negative powers last, because then we don't need to work with fractions. Also, here, I have noticed an interesting property about the number 125 - it's a cube number! Specifically, 5 cubed! So I will do power of 1/3, which is a cube root, first, to make things nice and simple for myself.

Now we just need to do our powers, one by one, to complete the question.

1251/3 = cube root of 125 = 5.
52 = 25.
25-1 = 1/25.

And we have our answer, 1/25!

If any of this has been confusing, I'd be happy to explain further!
If want to revise the rules in your own time, the BBC website has a great resource on them  here: http://www.bbc.co.uk/education/topics/zxkw2hv.

Joe R. 11 Plus Maths tutor, A Level Maths tutor, 13 Plus  Maths tutor...

8 months ago

Answered by Joe, a GCSE Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

442 SUBJECT SPECIALISTS

£18 /hr

Abigail L.

Degree: bsc politics and international relations (Bachelors) - Exeter University

Subjects offered: Maths

Maths

“About me: I am a third year politics student at the University of Exeter. Mathematics is something I am very familiar with, as I have done Additional Mathematics for my GCE O levels, and then Mathematics for GCE A Levels, and scored A...”

MyTutor guarantee

£20 /hr

Greg C.

Degree: Economics with Econometrics (Bachelors) - Exeter University

Subjects offered: Maths, Further Mathematics + 2 more

Maths
Further Mathematics
English
-Personal Statements-

“I consider myself a very extrinsic, hardworking person. I like to get involved in as much as I can and this is another opportunity to try something new! At the University of Exeter I’ve involved myself in a vast range of societies inc...”

MyTutor guarantee

£30 /hr

James B.

Degree: Management (Bachelors) - Bristol University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
ICT
Chemistry

“Hi there! I am currently a 2nd year Management student at the University of Bristol. I originally took Computer Science but switched to Management after 2 years of study. During my school life I was always very Science-based, studying...”

About the author

Joe R.

Currently unavailable: until 11/08/2016

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered: Maths, .STEP.

Maths
.STEP.

“Hello! My name is Joe, I’m a final year Maths student at the University of Warwick, and I am very excited to help you improve your confidence in maths regardless of your starting level. Maths can be one of the most daunting, confusin...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Why is it that when I am asked to factorise 3x^2-13x-10, I am not able to cancel two of the x's so that the answer is 3x-13-10?

How do I know when a quadratic function crosses the y-axis?

What's the difference between the mean, median and mode?

Sarah’s collection contains dresses, skirts and blouses. If the ratio of dresses to skirts is 7 to 4 and the ratio of skirts to blouses is 7 to 2, what is the ratio of dresses to blouses?

View GCSE Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok