For which integers a, b, c does a 2 b 2 c 5 a 2 (b 2 c)?
Justify your answer.
To find the integers a, b, and c that satisfy the equation a^2 * b^2 * c^5 = a^2 * (b^2 * c), we can start by simplifying the expression.
First, we can divide both sides of the equation by a^2:
b^2 * c^5 = b^2 * c
Next, we can divide both sides of the equation by b^2:
c^5 = c
Since c is raised to the power of 5 on the left side and only raised to the power of 1 on the right side, we can conclude that c must be 1. This is because any non-zero number raised to the power of 5 is still non-zero, while any non-zero number raised to the power of 1 remains the same.
Now that we have c = 1, we can substitute this value back into the original equation:
a^2 * b^2 * 1^5 = a^2 * (b^2 * 1)
Simplifying further, we obtain:
a^2 * b^2 = a^2 * b^2
This equation holds true for any values of a and b.
So, to answer the question, the equation a^2 * b^2 * c^5 = a^2 * (b^2 * c) is satisfied for any integers a, b, and c, provided that c = 1.