I learnt that there shouldn’t be a negative exponent and in order to make it positive, i have to recipricate it. Which means i have to flip it from the numerator to a denominator or vice versa, depending on where the negative exponent is located.

Ex.

As we can see here, has to be changed to a positive exponent. in order to do this, we must flip the variable with the exponent.

Therefore,  —

Now that my exponent is positive, I can work from there

If the negative exponent is in a fraction, we must only flip the variable with that exponent to the bottom or top. i use to get confused and flip the whole fraction but i now know i only flip the variable with the exponent unless if theres a bracket.

Ex.

Instead of flipping the whole fraction, we only need to bring down to the denominator because we only need to change that exponent, not the others.

Therefore, it will become

Converting to entire radicals to mixed radicals & Converting mixed radicals to entire radicals was what i had the most difficulty this whole unit. It was very confusing for me to convert as i would keep using the method for converting for one of them for the other one. I learnt that to convert entire radicals to mixed radicals, i’d have to multiply inside the radicand. It is a little confusing to explain in words so here is an example.

If i want to convert √108 to a mixed radical, 

√108 = √36 x 3               — I would find a number which can multiply into 108 that is square root

= √36 x √3            — I will separate it but it is still the same as √36 x 3

= 6 x √3                  — i will find the square root of 36 which is 6 and multiply it by √3

= 6√3                       — The answer is 6√3

To know if its the simplest form you have to make sure that the perfect square is the lowest perfect square it can be because or else it would not be the simplest form.

If i want to convert mixed radicals to entire radicals, i would need to bring the coefficient inside the radical number.

Ex. If i want to convert 3√14 to an entire radical,

3√14 = √3² x √14         — I would bring in 3 (coefficient) into the radical and square it

= √ 9 x 14            — therefore 3² = 9 so now we can multiply 9 x 14

= √126                  — the entire radical of 3√14 is √126

I still think i need to improve in this area but i now understand how to do it and i think i have really improved since i first started

 

I never knew what LCM (Least common multiple) was until not long ago when i found out what it is and how to do it. I get very confused with LCM and GCF (Greatest Common Factor) and i would get them both mixed up. LCM is the lowest multiple that the two numbers or more can multiply into together. For example, to determine the lowest common multiple of 10, 12 and 14, i would have to find the prime factors of each number, take all the prime factors of one of the numbers and multiply by any additional factors in the other numbers

10 = 2 x 5

12 = 2 x 2 x 3

14 = 2 x 7

Take 2 and 5 from 10

take 2 and 3 from 12

and 7 from 14

You then have to multiply then altogether and that will determine the LCM of 10, 12 and 14

2 x 5 x 2 x 3 x 7 = 420

The Least common multiple of 10, 12 and 14 is 420.

I used to get confused and multiply all the factors together but that is not the case, i have to multiply the prime factors