So everyone has his own approach for explaining something. It doesn't mean it's wrong. But what it means is that you have your own perspective on things. 

What am I going to show? 

What I am going to show is this idea that came to my mind, and I think it is fun to calculate 2⁴, 2⁵, and 2⁶ as high as you think you can go. 

Is it a new math formula? Does it prove something new? No. But it's a fun way to be creative and have fun. 

My idea

We all know 2⁵ is 2×2×2×2×2 = 32, 2 multiplied by itself 5 times. 

My approach is this:

a¹ = a + a 

a² = a¹ + a¹

a³ = a² + a² 

a⁴ = a³ + a³

a¹ = 2 + 2 = 4 

a² = 4 + 4 = 8 

a³ = 8 + 8 = 16

a⁴ = 16 + 16 = 32 

What does it prove? 

That it's a fun way to try and find solutions for problems in your own way of calculation. 

Seeing the world from your perspective. 

Conclusion 

Not everything we do must be a world changer. Sometimes we have to do things to have fun and enjoy ourselves.