How to Solve Problems involving Fractional Powers

Fractional powers appear past GCSE maths papers. To get the questions right, you must know how to use the Index Law, Surds and rules for solving the algebraic problems. 

This may sound overwhelming, but it is not that hard. See the illustrations (x3 questions) below.

How to Solve Fractional Powers Using Index Laws & Surds

If you need more illustrations like these, check out the free maths resources here.

Let’s have a look at 3 Higher Maths Exam Questions

how to solve fractional powers in algebra wjec maths gcse

Top tip:
All you need to do is to pull apart the powers and simplify them.


Download GCSE Maths past papers

You can download the past GCSE exam papers online. Here are some websites that many students prefer to use.

  • Maths Genie
  • Maths Watch
  • Dr Frost maths
  • Cobette Maths
  • GCSE maths in four weeks

Stationery items you will need for exams are available here: GCSE maths stationery items

Show your working out clearly and logically. Where there are 3 or more marks, do not only write the answer.

Lae School Fights (iv): Principals Face Dismissal If Schools’ Performance Does Not Improve

The UK government plans to create a body called regional school commissioners who will have powers to siege control from school identified as ‘failing’ by school inspection body Ofsted. The Independent  newspaper opening headlines read ‘ Government-appointed officials to remove governors and head teachers in failing schools….’ (18/10/2014). Under their control they will send 1500 ‘super teachers’ into struggling classrooms in an effort to boost students’ performance and improve schools’ ranking.

The whole idea was to challenge school governors, principals and deputy principals to pull-their-socks-up.


Lae city schools have senior education officers who have been sitting at the principal’s seats with years of experience. Some even feel as if they are irreplaceable. It is time Morobe Provincial Government comes up with a plan to challenge principals and deputy principals of troubled schools within the city.

This is not only about fighting against schools fights. It is also about improving schools’ academic performance - about improving ranking of Lae city schools.

So, if school governors and admins need motivation it must come from Morobe Provincial Government. The Government must take ownership of the schools in the province and step on the administration toes – show them who is in charge here.

Running a city school is not an easy task. This is clear from the onset, no one can deny it. But, governors and head teachers should be the force that drives a positive change, instead of being complacent. Why occupy a position in the admin when schools academic results are failing? Why doing the same thing over again when it didn’t work the first time?

 In fact, school governance must be based on systematic and workable guidelines - the school policies. Most schools do have all the policies that Education Department wants of them. These policies are cut and paste from national department’s documents with limited or no effect at school level. By this I mean, every school should look at ways to refine their policies to meet their needs.

What must school administrators do to improve school performance?

Drop in the number of Lae secondary school students going to tertiary institutions in successive years showed that there was urgent need to seriously reconsider the way things are done. Take a look at these as examples. Call it Guides For Principals Of All Schools In Lae City.

1.      Selecting Students – Begin With a Good School Culture

I pointed out in my first article one of the ways students join generation groups is determined by the part of city they come from. Targeting feeder schools can be an effective way to create good school atmosphere and stop students fights on the streets.

If negative students’ culture begins at primary school, school admin should re-think the traditional selection process. Instead of accepting students from the mainline schools, they should take students from outside the city.

Take for instance, city secondary schools should offer privileged places for students from remote schools like Menyamya, Wasu, Salamaua, Dregahafen, etc. All the boarding spaces should be awarded to these students with certain conditions attached. If it means expanding boarding space to 70% boarding and 30% day, it must be spearheaded by the Government to see a change.

Day students must also have conditions attested to their spaces. For example, parents must be from the working class or earning a certain amount of money in wage or salary, students must be living with a parent/s, students must be dropped off and picked up etc.

These are hints and examples for controlling enrolment and ensuring quality of students are maintained during selection of students.

(*Principals, you cannot stop students when they are fighting and killing each other at Eriku but you can stop it from happening)


2.      School Behaviour Policy – the code of conduct

This policy governs students’ ethos in classroom and around school. It is the code of conduct. They must be taught the requirements of being a student in a city school on day one: uniform, appearance, conduct, respect for teachers, respect for fellow students, respect for the public, etc.

The reason why a policy on code of conduct is important is that it neutralises bad behaviour students may have inherited from outside. When students come into a school they MUST pick up the school’s way of doing things, practice it and perfect it before they leave. This is how school influence students and prepare them to face the World.

One way to effectively implement such policy is to actually police it. That means that principals should know how to monitor students; they should know how to stop bad behaviour repeating; they should also know how to stop bad behaviour from spreading.

If it means doing random blood test on students to check for presence of illegal substance, by all means, school must do it. If it means suspending 25 students for the sake of 100, principals must take this bold step.

Perhaps the most important thing is to monitor, curtail and contain bad behaviour within schools.

(*Principals, you can create a way to neutralise bad students’ behaviour by putting in place a clear code where every student can follow from day one).


3.      School Disciplinary Policy – The Penalty

Disciplinary policy edges on the action school administration (including BoG) takes when a student has bridged School Behaviour Policy. This outlines what penalty one would have faced.

I clearly outline the step in taking disciplinary action in my third article and mentioned termination should always be considered as the last resort. Every opportunity has to be given to correct bad behaviours before this final action is taken.

In regards to Lae schools, a clear message has to go out to parents. They have to be made to sign a declaration to protect their child/ren. This means that parents have to agree with school’s code of conduct (School Behaviour Policy). By doing this parents agree to let school monitor and correct any behaviour contrary to schools' best practice.

END: Board of Governors and school administrators in Lae city schools MUST think about how to improve their school’s performance. Start fighting bad student behaviours. Create workable school policies to encourage good behaviour. This is a big challenge for all the principals and deputy principals in Lae city schools.

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I will give a summary of articles (i) - (iv) in my final post. 


4500 Spaces at Tertiary Institutions in PNG are Susceptible to Bribery

According to the Papua New Guinea Education Secretary, 21430 Grade 12 students have sat the national examinations this year. Dr Tapo also revealed that only 4500 spaces are available for the academic year 2015 at all higher learning institutions. That means that 20% of students in Grade 12 will be considered for universities and colleges throughout the country.

Tiri Kuimbaku's photo | Sharp Talk (Click to view discussion)

This article featured in PNG Attitude


The drop-out figure could be more than 80% (16730). Take a look at the data and facts presented. The irregularities are pretty shocking!

English and Literature (E&L) exam are compulsory/mandatory for all students. That means that if 21430 students have sat for the examinations, the same number should ALSO do the E&L exam. Unfortunately, the real number that sat the exam was put down to only 17236. So, who are those  4194 (i.e. 21430 - 17236) students?

In fact, the same number (21430) should also have sat for Mathematics examinations. The department statistics showed that 7091 students sat for Maths A and 13191 Maths B. That gives a total of 20282. Who are 1148 (21430 - 20282) students, where is their place in the total given by Dr Tapo?

Numbers presented by the secretary do not actually add up when we are talking about only 4500 spaces. 

Take, for instance, the difference between the total of grade 12 students given by the secretary (21430) and those sitting E&L (17236) is about the same as the number of spaces available from tertiary institutions, i.e. 4500 available spaces vs 4194 unaccounted students sitting the exams.

In the Maths exams, there are 1148 students who are suspiciously unaccounted for. We are talking about numbers in the thousands when there are only 4500 places. The odds indicated that dropout figures for this year could be more than what initially thought.

As a matter of clarification, students doing code, distance study or resitting exams could have been included. 

But, even if they are included the irregularity is in the thousand and so there is a stiff competition between the 'known' and 'unknown' students, the accounted and the unaccounted. That means that more than 4000 students who are not attending a formal secondary school are also vying for one of the 4500 spaces.

Fair enough. But, the secretary for education should make this clear in his reporting. He is presenting figures that do not reflect the actual situation. How many students are not from the mainstream education system? At least put some meaning into the numbers.

The irregularities in numbers do indicate extra students are included in the total competing for the limited spaces. So who are they? We don't know. The point is: if 4000 students from the mainstream secondary school are competing for the 4000 spaces with another 4000 'ghost' students, the NET competition is zero.

In reality, those 4500 spaces are susceptible to bribery, manipulation and foul-play of all sorts. So, who suffers here?  Those poor students who have spent the best part of their 12 years in the formal education stood little or no chance against a manipulative (unaccounted) lot. 

The Papua New Guinea Department of Education needs to collect relevant and accurate data from schools around the country. The secretary analysis must base on factual data. He must not spit out data to the media when the numbers are flawed.

Make no mistake. The unambiguous numbers can have a dramatic effect on mainstream students - those young 18 and 19 years old. It is unfair to mistreat one student in the selection process, let alone thousands of them. 

END: PNG education system is producing 80 - 90% dropouts at Grade 12 every year. Yet, the government does not have accurate data to help sort out this problem.

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Port Moresby's Best Getaways Top Things to Do

POM has lots of things visitors can do. Like any holiday, if you do proper research, you are likely to find the best things around/within the city to do. 

I thought it would be helpful to list 10 touristy 'things' visitors (including locals) can do when in POM.

port moresby adventure park crocodile


5 Things To Do in Port Moresby

1) You can arrange for a guided tour along the ranges from UPNG to Hanubada (a good way to see POM from a different angle) or singsing group from one of the Motu Koitabu villages (travel out to the village and enjoy the tranquillity there). 

2) The  Parliament House -Opens every weekday, free f charge. You can look around or go in when the doors are open and visit Parliament Gallery. Check parliamentary sitting time. If you love comedy, you'll enjoy the sessions - a must-watch. 

3) Port Moresby Botanical Gardens - Variety of native flora and fauna to see at the gardens: Animals can be seen up close and personal; Cassowary, Bird of Paradise, Crocodile, Snakes, including a good collection of ferns and orchids. 

4) Vision City Mall - If you are up for a stroll or window shopping, VCM could be the right place to visit. It offers a contemporary shopping experience. (Ssshhh....here is the secrete: given the value of PNG Kina at the moment, overseas visitors can shop and save). Paradise Cinema is located within its precincts- check out the cinema if you want to watch dull movies. 

5) Ela Beach Art and Craft Market - takes place either at the end or beginning of every month. A lively atmosphere, always buzzing with traditional items, PNG bilums, carvings, canvas paintings and all things PNG. You may see a traditional PNG 'singsing' performing at the market. 

5 Things To Do Outside Port Moresby, a Drive away

port moresby getaway

6) Loloata - day visit to Loloata Island Resort can be arranged easily from any hotel in POM. Spending a day or two is not a problem as there are plenty of activities you can do when on the island: snorkelling, diving, walking, kayaking, or just relaxing in the sun - recommended.

7) Kokoda - If you really want to feel the tropical heat and enjoy the flora and fauna. You've got to do this. Preparation is essential. Tour operators can be found here.

8) Pacific Adventist University Sunday Market - take a trip out to PAU, and enjoy the Sunday morning market and surroundings there. You can also visit the Safari Park while you are there (right at the entrance to PAU) or travel 10 minutes up to Crystal Rapids & to Bomana War Memorial. A complete package can be found on the PNG Trekking Adventures website.


9) Varirata National Park - You don't have to travel to other parts of PNG to see beautiful birds of paradise and enjoy the natural beauty of the place. A day trip to VNP is a better way to get out of the city. 

10) March Girls Resort - Located 3 - 4 hours out of the city, a nice place with a 'black sandy beach'., a good family getaway. Along Magi Highway, travelling past Loloata. There are roadside markets where you can get fresh 'kulau', watermelon, mango and anything on sale at a fraction of the price in POM. Take a picnic, sit on the beach, have an SP beer and enjoy the day.

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