Exponentiation distribute over addition

Question

Which equation is true?

 

1. (a+b)^n=a^n +b^n

2. (axb)^n=a^n x b^n

 

For the one that is not true can you provide a counter example. For the one that is true can you explain that also.

 

Answer 1

Equation (2) is correct.

 

(ab)ⁿ = aⁿbⁿ

 

Equation (1) represents one of the most common errors made by algebra students.

Answer 2

Counter example for Equation 1: 

a = 5, b = 10, n = 2

(5 + 10)² = 15² = 225

5² + 10² = 25 + 100 = 125

225 does not equal 125