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a^m = a × a × a × a ... (m times)

a is referred to as the base and m is referred to as the power

a⁰ = 1 (any number to the power 0 is always 1).     Eg. 2⁰=1, 100⁰=1

a¹ = a (any number to the power 1 is always the number itself).     Eg. 2¹=2, 100¹=100

a² = a × a.     Eg. 2²=4, 10²=100

a³ = a × a × a.     Eg. 3³=27, 10³=1000

a⁴ = a × a × a × a.     Eg. 5⁴=625, 10⁴=10000

a⁵ = a × a × a × a × a.     Eg. 2⁵=32, 10⁵=100000

a^m × aⁿ = a^m+n

Eg.     2³ × 2⁴ = 2⁷

Eg.     3² × 3³ = 3⁵

a^m / aⁿ = a^m-n

Eg.     2⁴ / 2² = 2²

Eg.     4⁵ / 4² = 4³

a^m × b^m = (ab)^m

Eg.     2³ × 4³ = 8³

Eg.     5² × 3² = 15²

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

Eg.     8³ / 4³ = 2³

Eg.     8² / 3² = (8/3)²

(a^m)ⁿ = a^mn

Eg.     (2²)⁴ = 2⁸

Eg.     (3²)³ = 3⁶

a^{− m} = 1 / a^m

Eg.     2^{− 3} = 1 / 2³

Eg.     3^{− 4} = 1 / 3⁴

a^m = 1 / a^{− m}

Eg.     2³ = 1 / 2^{− 3}

Eg.     3⁴ = 1 / 3^{− 4}