+2

# Why is line 11 = 1? I feel like I'm missing some math rule...

https://code.sololearn.com/cKMykOhd8qvE/?ref=app

2/5/2020 4:12:31 AM

Dina Stendig

+4

negative 1 to an even power is positive 1. For example, (-2)*(-2)=+4

+2

Any number? It's * a 6 digit #...

+2

6 to the power of 7 is a 6 digit even number.

+2

w(-1) raised to this large even power gives +1.

+2

Just additionally listing the math rules for clarity. Would you agree to all of the following? i) n**(j*k) = (n**j)**k = (n**k)**j ii) (j*k)**n = j**n * k**n iii) 1**n = 1, for all natural numbers n iv) (-1)**2 = 1 v) n is even, if and only if it is divisible by 2. Hence, if and only if there is an m such that n = 2*m If so, then let n be an even natural number. From the above we get: (-1)**n = (-1)**(2*m) (by v) = ((-1)**2)**m (by i) = 1**m (by iv) = 1 (by iii) So, yes, for all even natural numbers n, (-1)**n = 1. Now observe in your case that w is -1. And further that, by (ii), 6**7 = (2*3)**7 = 2*(2**6 * 3**7), thus 6**7 is an even number.