Why are the answers for x^18=10^18 and x^21=10^21 different?

Question

Why are the answers for x^18=10^18 and x^21=10^21 different?

When I put both equations in a mathsolver website:

for x^18=10^18, i get x=10 and x=-10

for x^21=10^21, i get only x=10

does anyone know why?

Answer 1

Hello Roland,

You’re getting an additional answer for x^18 = 10^18 because 18 is an even exponent while 21 is odd.

If you raise a negative number like -10 to an even exponent (like 18), the answer will be positive.

A negative number (-10) raised to an odd exponent (21) gets you a negative answer.