LCHL Indices

These lessons will involve the students in investigating, understanding & solving problems using:

• the rules for indices (where a, b ∈ R; p, q ∈ Q; ap, aq∈ Q; a, b ≠ 0):

• a^pa^q = a^p+q

• a^p/a^q = a^p-q

• a⁰ = 1

• (a^p)^q = a^pq

• a^1/q = ^q√a (q ∈ Z, q ≠ 0, a>0)

• a^p/q = ^q√a^p = (^q√a)^p (p,q ∈ Z, q ≠ 0, a>0)

• a^-p = 1/a^p

• (ab)^p = a^pb^p

• (a/b)^p = a^p/b^p

Alison.com

Adding and multiplying simple powers

Working with indices

Negative indices

Fractional indices, numerator of 1

Index power equal to 0

Positive fractional indices all types

Negative fractional indices

Large numbers in standard form

Changing decimals to standard fom