Question

0 to the power of 0 is?

Answer 1

The expression 0⁰ is said to be in indeterminate form. Its value cannot be determined definitely.

When we try to find the value of an algebraic expression or function, we use limit if it is not possible to determine the exact value. This concept will be study in higher classes

Let’s review two rules of mathematics:

• 0ⁿ = 0
  • zero to any power is equal to zero
• nº = 1
  • any number to the zero power is equal to one

Do you see the conflict?

• Depending on which law you use, 0º has TWO DIFFERENT VALUES

That is why we say that 0º is indeterminate, and why most calculators will generate an error message (see the last image below for an example).

What does the value APPROACH?

In Calculus, you will learn that nⁿ (n to the nthth power) approaches ONE as n approaches zero, but ONLY as n approaches zero FROM THE RIGHT. In Higher Classes