Mathematics?

Question

Why does 10^0 equal 1

Should it not equal 0?

Answer 1

Think about it like this:

10^1 = 10
10^2 = 10 * 10
10^3 = 10 * 10 * 10
10^4 = 10 * 10 * 10 * 10

Now do it backwards:
10^4 = 10 * 10 * 10 * 10
10^3 = (10 * 10 * 10 * 10)/10 = 10 * 10 * 10
10^2 = (10 * 10 * 10)/10 = 10 * 10
10^1 = (10 * 10)/10 = 10
10^0 = 10/10 = 1.

Also, when you define negative exponents, you're dividing:
10^(-1) = 1/10
10^(-2) = 1/100
And so on and so forth.

When you multiply by 10, you add one to the exponent.
When you divide by 10, you subtract one from the exponent.

Based on these properties, 10^0 = 1.

Answer 2

Look at the number line, starting with 1000 and going backwards by powers of ten: 1000=10^3, 100=10^2, 10=10^1, 1=10^0, 1/10=10^-1, 1/100=10^-2, 1/1000=10^-3 and so on to 10^-infinity, which if infinity was a number would be equal to zero.

Answer 3

Any number to the power of zero = 1
Consider powers of 10 as shown below:
10³-----10²---10^(1)----10^(0)
1000---100----10-------1
From above , the numbers on the bottom line are obtained by dividing the previous number by 10.

It would then suggest that 10^(0) = 1

Answer 4

10^0=1 because 10^1, 10^2 and so on coul be said as 10*10*1 or
10*1 and 1 could be the invisible factor. So therefore, if 10 is not multiplied, 1 is still there

Answer 5

it is because you take away a zero. For example 10^5 is 100,000, 10^4=10,000 10^3=1,000 10^2=100 10^1= 10 so 10^0 =1 because there is no more zeros

Answer 6

Every number ^0 equals 1, it is a mathematical rule.

Answer 7

To prove x^0=1, where x belongs to the set of real numbers.

Since we know x^y/x^z=x^(y-z)

x^0=x^(y-y)=x^y/x^y=1

To make things and to make numbers follow the rule x^y/x^z=x^(y-z), mathematicians made it so that x^0=1,it is just how it is defined.

Answer 8

because 10/10 = 1

we write (a^m)/a^n = a^(m -n) so if m = n we have a^0 but that simply means that we have 1.