How can we know from the prompt that y=0 or y=1. I don't understand that.
Thanks to explain.
Exponents and roots
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Given that m and k are non zero integers, m + k cannot equal m.didieravoaka wrote:If m and k are non zero integers and yáµ�â�ºáµ� = yáµ�, what is the value of y?
(1) k is odd.
(2) y is odd.
Most numbers generate different numbers when raised to different powers.
The only numbers that can generate the same numbers when raised to different powers are 0, 1 and -1.
So there are only three values of y that could work in the equation yáµ�â�ºáµ� = yáµ� , y = 0, y = 1 and y = -1.
0 and 1 raised to any power generate 0 and 1.
-1 raised to any even power generates 1. So if m is even and m + k is even, -1áµ�â�ºáµ� = -1áµ�.
-1 raised to any odd power generates -1. So if m is odd and m + k is odd, -1áµ�â�ºáµ� = -1áµ�.
Statement 1: k is odd.
This tells us that y â‰ -1.
If y = -1 and if m is even and k is odd, then m + k is odd. So yáµ� = 1 and yáµ�â�ºáµ� = -1.
If y = -1 and if m is odd and k is odd, then m + k is even. So yáµ� = -1 and yáµ�â�ºáµ� = 1.
So if k is odd, yáµ�â�ºáµ� cannot be equal to yáµ� if y = -1.
Still, y could be 0 or 1.
Statement 2: y is odd.
This tells us that y cannot be 0, but y could be 1 or -1.
Combined the statements tell us that y is not 0 or -1. So y must be 1.
The correct answer is C.