How do you simplify 9^0?

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Answer 1 · 2015-09-09T13:35:43

#9^0 = 1 #

Anything raised to #0# is equal to #1#.

To see why, let's first consider how we increase the exponent of a number, by multiplying.

#9^1 = 9#
#9^2 = 9 xx 9#
#9^3 = 9 xx 9 xx9#
#...#

So, to decrease the exponent of a number, we divide.

#9^3 = 9 xx 9 xx 9 #

#9^2 = (9 xx 9 xx9)-:9= 9xx 9 #

#9^1 = (9 xx 9)-:9= 9 #

And if we take it one step further:

#9^0 = 9 -:9= 1 #

We can actually take it even further, and end up with negative exponents.

#9^(-1) = 1 -:9= 1/9 #

#9^(-2) = 1/9 -:9= 1/81 #

#...#

So you can see why #9^0 = 1 #.