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Fractional powers

Laws of Exponentiation

For all fractions and and

Law 1

a^m/n X a^p/q = a^{m/n + p/q}

Example

3^1/2 X 3^1/3 = 3^{1/2 + 1/3}

Law 2

(a^m/n)^p/q = a^mp/nq

Example

(2^1/2)^3/5 = 2^3/10

Law 3

= a^{m/n - p/q} if > and a 0

Example

= 5^{3/4 - 1/4} = 5^1/2

Law 4

= if < and a 0

Example

= =

Law 5

(a X b)^m/n = a^m/n X b^m/n

Example

(2 X 3)^1/2 = 2^1/2 X 3^1/2

Law 6

()^m/n = and b 0

Example

()^1/2 =

Before proceeding to the exercises, ensure that you have a pencil and some paper handy.


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