prove that x^0=1
answered below.
Look under the question by lee just a few problems below.
Since a^m x a^n = a^(m+n) for all values of m and n, by replacing the exponent m by 0, we get
a^0 x a^n = a^(0 + n) = a^n
Then, a^0 = a^n/a^n = 1.
Therefore, any quantity with a zero exponent is equal to 1.
To prove that x^0=1, we can use the exponent properties and algebraic manipulation.
1. Start with the expression x^0.
2. Use the property that a^0 = 1 for any non-zero number a. This property states that any non-zero number raised to the power of 0 is equal to 1.
3. Therefore, x^0 = 1.
In the given answer, the property a^m x a^n = a^(m + n) is used. By replacing the exponent m with 0, we get a^0 x a^n = a^(0 + n) = a^n.
Using this property, we can rewrite x^0 as x^n/x^n, which equals 1. Therefore, x^0 = 1.
It's important to note that this proof is applicable for any non-zero number x raised to the power of 0.