Do these eqations equal each other? a ^ ( b * c ) = ( a ^ b ) ^ c

Test it out if you're unsure. I have to do this a lot to check myself. Just pick some random numbers for a, b, and c and test it.

 

I pick a = 2, b = 3, and c = 4

2 ^ ( 3 * 4 ) = ( 2 ^ 3 ) ^ 4

2 ^ ( 12 ) = 8 ^ 4

4096 = 4096

So yes they are equal.

 

You can see why too:

(2³)⁴ = (2³)(2³)(2³)(2³) = (2)(2)(2) (2)(2)(2)​ (2)(2)(2)​ (2)(2)(2)​ = 2¹²