- #1
yungman
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What is [tex]x^0[/tex] when x=0?
My thinking [tex]0^0=1[/tex]
Am I correct? Why?
My thinking [tex]0^0=1[/tex]
Am I correct? Why?
Last edited:
Hurkyl said:The problem is that you are mixing up two different kinds of exponentiation. (Alas, the difference is usually not mentioned. )
"xn" the monomial and "xn" the real number are different expressions describing different types of objects. However, monomials can be converted into functions, and expressions in a variable can be converted back and forth with expressions denoting a number, and most of the time it doesn't matter how you interpret things.
Alas, the monomial "x0" is the same as the monomial "1", and so the associated function is f(x)=1 with domain all of R.
But the real number "x0" (with exponentiation interpreted as real exponentiation) is only partially defined -- at best, the variable x must be restricted to nonzero reals.
Generally speaking, though, the only time you would ever encounter 00 is when you were working with monomials, which is why people sometimes adopt a convention that extends real exponentiation so that 00=1.
When x is raised to the power of 0, the result is always 1 regardless of the value of x. Therefore, x^0 = 1 when x=0.
No, x^0 is not undefined when x=0. As stated earlier, any number raised to the power of 0 is equal to 1, so x^0 = 1 when x=0.
This is because any number raised to the power of 0 is defined as 1. This is a mathematical rule and applies to all numbers, including 0.
No, x^0 can only be equal to 1 when x=0. This is a fundamental mathematical rule and cannot be changed.
Raising a number to the power of 0 has various applications in mathematics and science, such as simplifying equations, finding limits, and calculating derivatives. It is also a fundamental rule in exponent laws and helps in solving various problems in these fields.