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Indices and Surds
Multiplying with indices
To multiply indices you add the powers
a² x a³ = (a x a) x (a x a x a) = a²˖³ = a⁵
Dividing with indices
To divide indices you subtract the powers
a⁵ ÷ a³ = (a x a x a x a x a) ÷ (a x a x a) = a⁵⁻³ = a²
Power raised to a power
When a power is raised to a power you multiply the powers
(a³)⁵ = a³˟⁵ = aᶦ⁵
Fractional powers
In a fractional power the denominator (the bottom power) is the root
a⅓ = ₃√a
Negative powers
A negative power means the reciprocal of the number
a⁻² = _1_
a²
Fractional and negative powers
When the power is both negative and a fraction the fractional power is dealt
with first and then put to the reciprocal