Powers, roots and laws of indices

The manipulation of powers and roots is a crucial underlying skill needed in algebra. In this video, powers and roots of numbers are explained, together with the laws of indices.
More on Laws of Indices here 👉: • Simplifying Algebraic ...
For more Mathematics videos, check out my playlist here 👉 • Maths
TIMESTAMPS:
00:00 Intro to Powers and Roots
01:54 Law 1
03:30 Law 2
04:06 Law 3
04:40 Law 4
05:07 Law 5
05:30 Law 6
06:09 Worked Examples - Combining the 6 laws

[@PhysicsTutoringHub]

Check out my next video on how to apply the laws of indices to solve algebraic expressions 👉 czcams.com/video/Ss2Z-Tpq9Ws/video.html

[@itzgelastic962]

good video, nicely explained all the laws

[@PhysicsTutoringHub]

Thank you, I'm glad it's helped itzgelastic

[@JustDiggaj]

nice video, perfectly explained

[@PhysicsTutoringHub]

Thanks I'm glad it helped you 😁

[@TheMadMagician87]

Quick question. At approx the 6 min mark, you say you must evaluate the root first, before evaluating the exponent. In your example, take the cubic root of 8 first, then square that result (yielding 4). As far as I can tell (just using the positive real numbers for root and exponent), it makes no difference what order one does it in (i.e. cubic root of 64, is also 4). Why do you say the root must be evaluated first?

[@PhysicsTutoringHub]

Hi, Good question. It all comes down to the order of precedence You might have come across the acronym PEMDAS or BODMAS (P = parentheses, E = exponents (and square roots), M = multiplication, D = division, A = addition, and S = subtraction.) So, just above the example at 06:02 we have the root within parentheses. Everything within parentheses must be evaluated first, so in the example, I cube root 8 first then square the result. But, even without the parentheses, the cube root and power are both exponents (E in the PEDMAS acronym). When you have two exponents together, you always calculate them from left to right. It's just the convention even though, in this case, you receive exactly the same result no matter what way round you sum them. It's confusing 😆

[@TheMadMagician87]

@@PhysicsTutoringHub okay, that makes sense, thanks. The rules, are the rules :)

[@PhysicsTutoringHub]

@@TheMadMagician87 Even if they are annoying 😄

[@jan-willemreens9010]

... Good day to you, I just finished watching your presentation, and at about time 1:30 I observed an accidental writing error regarding - 3^2 = 9 ... I'm pretty sure you meant ( - 3 )^2 = 9 ... - 3^2 = (- 1) * 3^2 = (- 1) * 9 = - 9 ... a very important difference in calculations between " ( - 3 )^2 " and " - 3^2 " ... but of course this is not new to you ! A good refresher presentation for my tutoring students (lol) ... Thank you, Jan-W

[@PhysicsTutoringHub]

You're absolutely right. Thanks, Jan-W, well spotted 😊 (Powers take precedence over multiplication/division; parentheses/brackets take precedence over powers). I'm sure I have plenty of other mistakes like this in these videos - If you spot any more, do let me know.

[@user-lh4jo5pl1e]

❤

[@PhysicsTutoringHub]

Thanks. I'm glad you liked it 😊