a^4b^5-a^5b^4=0

Solution for a^4b^5-a^5b^4=0 equation:

Simplifying
a4b5 + -1a5b4 = 0

Solving
a4b5 + -1a5b4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a4b4'.
a4b4(b + -1a) = 0

Subproblem 1
Set the factor 'a4b4' equal to zero and attempt to solve:

Simplifying
a4b4 = 0

Solving
a4b4 = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a4b4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(b + -1a)' equal to zero and attempt to solve:

Simplifying
b + -1a = 0

Reorder the terms:
-1a + b = 0

Solving
-1a + b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-1b' to each side of the equation.
-1a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-1a + 0 = 0 + -1b
-1a = 0 + -1b
Remove the zero:
-1a = -1b

Divide each side by '-1'.
a = b

Simplifying
a = b
Solution
a = {b}