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An exponential number is a function that is expressed in the form of , where x represents a constant, known as the base; and n, the exponent of the function, can be any number. The exponent defines how many times the base is multiplied by itself. For example, represents the operation .
Many students find it strange that anything raised to the power of 0 is 1. A lot of students think it should be 0, just like anything multiplied by 0 is 0. But remember, you are not multiplying by the exponent, but using the exponent to tell how many times to multiply a number by itself.
We can use the product of powers property to see exactly how the 0 exponent works.
We already know that . The product of powers property says that . If we try to multiply , we get 0, so can't equal 0. We do know that , so has to equal 1.
The general rule is that for all real numbers x where , we have:
We can also use the quotient of powers property to show that a number with a 0 exponent equals 1.
We know that using the quotient of powers property because when we divide numbers with the same base, we subtract the exponents.
That means that , and we already know that , so we can see that . That is, any number (except 0) raised to the power of 0 equals 1.
Note that is undefined.
Common Core: 6th Grade Math Flashcards
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