Question

What connection(s) can you make between the Quotient Rule and Zero as an Exponent Rule?

Answer 1

Step-by-step explanation:

For any nonzero real number  a  , the zero exponent rule of exponents states that  $a^{0} = 1$

In this case, we would use the zero exponent rule of exponents to simplify the expression to  1  . To see how this is done, let us begin with an example.

$\frac{t^{8} }{t^{8} } = 1$

If we were to simplify the original expression using the quotient rule, we would have

$\frac{t^{8} }{t^{8} } = t^{8-8} = t^{0}$

If we equate the two answers, the result is  $t^{0} =1$ . This is true for any nonzero real number, or any variable representing a real number.

$a^{0}=1$

The sole exception is the expression  $0^{0}$  . This appears later in more advanced courses, but for now, we will consider the value to be undefined.