- Index notation
- Scientific notation
- Prime factorisation
- Index laws
3 x 3 x 3 x 3 x 3 x 3 x 3 = 3⁷
a x 10ᵐ where m is an integer and 1 <= a < 10
Writing a number as a product of its prime factors.
108 = 2 x 2 x 3 x 3 x 3 = 2² x 3³
On Casio calculators, you can obtain the prime factorisation of any inputted number by pressing
SHIFT + DMS button.
On Sharp calculators, well, I don’t know.
aᵐ x bⁿ = aᵐ⁺ⁿ aᵐ ÷ bⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ (ab)ᵐ = aᵐbᵐ
See Fractional indices for fractional indices.
(a/b)ᵐ = aᵐ/bᵐ
a⁰ = 1 where a != 0
a⁻ᵐ = 1/aᵐ
a¹/ᵐ = ᵐ√a aˣ/ᵐ = ᵐ√aˣ
Surds are irrational numbers written with a radical sign. They cannot be expressed as a fraction.
5√6 is a surd. It means
5 x √6.
You can only add or subtract surds if they are like surds. For example, 5√6, 3√6 and √6 are like surds. If you were to add or subtract these together:
5√6 + 3√6 + √6 = 9√6 5√6 - 3√6 - √6 = 5√6
a√b x c√d = ab√cd √a / a \ –– = √| ––– | √b \ b /
What a beautiful attempt at making a big bracket. I’m not bothered to go to the bracket making website right now so you’re going to have to deal with it.