Final answer:
To explain why a^0 = 1 using properties of exponents, we can use the rule that when we multiply two numbers with the same base, we add the exponents. Applying this rule, we interpret a^0 as multiplying the number a by itself 0 times, which is equivalent to multiplying it by 1. Therefore, a^0 equals 1.
Step-by-step explanation:
To explain why a0 = 1 using properties of exponents, we can consider the rule that when we multiply two exponentiated numbers with the same base, we add the exponents. For example, 51 * 51 = 52. Since the exponents add up to 2, we interpret this as the square root of 5, which is equal to 5. Therefore, we can express the familiar friend a as a fractional power: x2 = √x.
Now, let's look at the rule for raising a number to an integer power. When we raise a number to a power, like 43, it is equivalent to multiplying the number by itself for the number of times indicated by the exponent. In this case, 43 means multiplying 4 by itself three times, which gives us 4 x 4 x 4 = 64.
Using these two rules, we can see that when a number is raised to the power of 0 (a0), it implies that we are multiplying the number by itself 0 times. And when we multiply any number by 1, the value of the quantity remains unchanged. Therefore, a0 = 1.