Why is any number to the power of zero equal to 1?

Question

Please supply an answer that's suitable for children. If possible! Ta.

Answer 1

It goes with the exponent rule of x^m/x^n = x^(m-n). When your variables match in a fraction, you subtract the exponents. In order to get a zero exponent, the exponents in the original fraction have to be the same. If the numerator and denominator are both the same, the fraction is equal to 1.

For example, x^5/x^5 = x^(5-5) = x^0 = 1

Answer 2

You must be knowing that any number divided my itself is 1. Say 2/2 = 1 then .. 3/3 = 1 and so on .. Now according to the rules of the power, when u want to divide the same number with different power, u substract the power of the denominator frm the power of numerator - To illustrate this : (8^5)/(8^3) = 8^(5-3) which makes it 8^2 = 64 Now consider a sum like 8/8 - you know the answer's 1 but it can also be expressed as 8^1/8^1 (because any number with power 1 is the number itself !) So according to the rules - 8^1/8^1 = 8^(1-1) = 8^0 = 1 (because 8/8 = 1) In this way it applies to any number ! Moreover, any number to the zero power means the number is being divided by itself.

Answer 3

Follow the pattern below.
4^3 = 64
4^2 = 16
4^1 = 4

So each time you subtract one from the power and divide the right side by 4 to get to the answer below it. So using that logic the next power would be 0 (1-1) and it would equal 1 (4/4),
4^0 = 1

This same pattern will work for any number that you want to with the exception of zero.

Hope this helps. :)

Answer 4

The explanation by PatsyBee and Curious is probably the best for children, but it is easier using multiplication than using their division.

x^a * x^b = x^(a+b)

Therefore x^a * x^0 = x^(a+0) = x^a

Therefore if x^0 is not 1, you are stuffed (I'm sure you can put that more nicely for the children).

Answer 5

that's mathematical rule. x to the 0 power equals 1 because X dose not equals 0.

Answer 6

the "zero"power" takes the one's place... the one next to the decimal.

thinking of the place values as exponents, the value next to the decimal is the ones place, must be represented by the zero power ....

10^2 (hundreds) ... 10^1 (tens)... 10^0 (ones) ....decimal point.... 10^(-1) tenths 10^(-2) hundredths and so on

the zero power holds the ones place, so ANY base to the zero power (base not equal to zero) is one.

Answer 7

When you divide x^a by x^b you get x^(a-b).
Now what do you get when a nad b are equal.
1= x^a/x^a = x^(a-a) =x^0
Thus we get anything to the power of zero is equalto one.