Why is it (-2.97)^0 and not 5^0 + 9^0 to result the answer to 1
Exponents have a specific set of rules that govern their behavior. One rule states that any number raised to the power of zero is equal to 1.
In the expression (-2.97)^0, we are raising the number -2.97 to the power of zero. Following the exponent rule, this expression equals 1.
On the other hand, in the expression 5^0 + 9^0, we are evaluating the sum of 5 raised to the power of zero and 9 raised to the power of zero. However, applying the exponent rule, both 5^0 and 9^0 would equal 1. Therefore, the expression simplifies to 1 + 1, which results in 2, not 1.
Thus, (-2.97)^0 evaluates to 1, while 5^0 + 9^0 equals 2.
The reason (-2.97)^0 is equal to 1, while 5^0 + 9^0 is not, is due to the properties of exponents.
Any non-zero number raised to the power of 0 is defined to be equal to 1. In other words, for any non-zero number a, a^0 = 1. This is a fundamental rule in mathematics.
On the other hand, when we have addition or subtraction of exponents, such as 5^0 + 9^0, the properties of exponents are different. Exponents are applied to the base number, and then we perform the operations like addition or subtraction. In this case, both 5^0 and 9^0 would be equal to 1 individually, but the addition of these two values would give us 2, not 1.
So, to summarize, (-2.97)^0 is equal to 1 because any non-zero number raised to the power of 0 is defined to be equal to 1. However, 5^0 + 9^0 is not equal to 1 because the addition of exponents does not follow the same rule as raising a number to the power of 0.
To understand why (-2.97)^0 is equal to 1 while 5^0 + 9^0 is not, let's first review the basic rules of exponents.
Any number raised to the power of zero is always equal to 1. This means that for any positive number, negative number, or zero, x^0 = 1.
Now, let's investigate the two examples you provided:
1. (-2.97)^0:
In this case, we have -2.97 raised to the power of zero. Since any number to the power of zero equals 1, (-2.97)^0 = 1.
2. 5^0 + 9^0:
In this case, we have 5 raised to the power of zero, plus 9 raised to the power of zero. According to the rule we discussed earlier, both 5^0 and 9^0 should equal 1. However, the expression 5^0 + 9^0 does not represent raising each number to the power of zero separately and adding the results. Instead, it represents adding the values of 5^0 and 9^0 together, which would be 1 + 1 = 2.
To sum up, the correct representation of raising a number to the power of zero is x^0 = 1. However, when you see an expression with multiple terms involving exponentiation, you cannot distribute the exponent directly to each term. Each term must be evaluated separately before performing any operations between them.