Power of a Power

Consider the following:

(x^m)ⁿ

x^m multiplies x, m times. And (x^m)ⁿ multiplies x^m, n times. Thus, (x^m)ⁿ multiplies x, m ⋅ n times.

x^{(m ⋅ n)} also multiplies x, m ⋅ n times. Thus:

(x^m)ⁿ = x^{(m ⋅ n)}

Here are some examples:

(2³)⁴ = 2^{3 ⋅ 4} = 2¹²

((a + 3)⁶)⁹ = (a + 3)^{6 ⋅ 9} = (a + 3)⁵⁴

Comments

Please log in to add comments