what is the anwer to 22^0*22^4

Question

please explain your answer.

Answer 1

Hi Andrew;

Any integer to the power of 0 is 1.

22⁰*22⁴

1*22⁴

22⁴

Answer 2

any number(except 0) raised to the 0 power is equal to the number 1

0 raised to the 0 power does not exist in mathematics

 

look at some examples:

 

1000/100=10, or 10^3/10^2=10^(3-2)=10^1=10

 

100,000/1000=100, or 10^5/10^3=10^(5-3)=10^2=100

 

10^a/10^b=10^(a-b)

 

the base does not have to be 10, it can be any number (except 0)

 

2^5/2^3=2^(5-3)=2^2=4, 32/8=4

 

5^4/5^2=5^(4-2)=5^2=25, 625/25=25

 

10,000/10,000=1

10,000=10^4

10^4/10^4=10^(4-4)=10^0=1(remember 10,000/10,000=1 ?)

in general x^a/x^b=x^(a-b) where x is any number except 0 and any number divided by itself is 1(except 0 divided by 0 !!!)

 

12^7/12^7=1 and 12^7/12^7=12^(7-7)=12^0=1

 

in general x^a/x^a=x^(a-a)=x^0=1 where x is any number except 0

 

 

Answer 3

How do we know that any number raised to the zero power = 1?  Suppose we hade the following problem:

 

Xⁿ / Xⁿ  = 1

 

Now we know that moving the term in the denominator to the numerator requires changing the sign of the exponent.

 

Xⁿ * X^-n = 1

 

 

Now we also know that multiplying two like terms together requires that we add the exponents.

So n + -n =0 and we end up with X⁰ = 1.

 

So any number X raised to the zero power is 1.