a^0=1.
1^1=1
1^0=1
also when the bases are same the powers can be equated.
=>1=0.
2006-10-13 03:32:38 · 4 answers · asked by Charu Chandra Goel 5 in Science & Mathematics ➔ Mathematics
The index law
a^x=a^y
x=y is valid only when base is not equal to one.
otherwise we can get absurd results
1^1000=I^10000000
so 1000=10000000 and so on
2006-10-13 03:52:22 · answer #1 · answered by openpsychy 6 · 0⤊ 0⤋
1^anything = 1... showing that 1 to two different powers doesn't mean that those powers are equal. That would be the same logic of saying that since 0*5=0 and 0*6=0 then 5 must equal 6.
2006-10-13 12:13:57 · answer #2 · answered by Kyrix 6 · 0⤊ 0⤋
Actually when you think about the lim a^x when x is approaching to 0 result also approaches to 0, however the equally of a^0=1 is just an assumption on the other hand this assumption contradicts with the question that you have asked so they simultaneously said that a^x = a^y => x = y when a does not equal to 1
2006-10-13 10:57:05 · answer #3 · answered by alp 1 · 1⤊ 0⤋
The property a^x = a^y => x = y can only be used when the base is not equal to 1.
2006-10-13 10:38:50 · answer #4 · answered by James L 5 · 1⤊ 0⤋