Question

evaluate \\(\frac{5^{-1}}{-9^{0}}\\). write your answer as a fraction in si
the solution is \\(square\\).

Explanation:

Step1: Simplify the numerator

Recall the negative exponent rule: \(a^{-n}=\frac{1}{a^{n}}\). So for \(5^{-1}\), we have \(5^{-1}=\frac{1}{5^{1}}=\frac{1}{5}\).

Step2: Simplify the denominator

Recall the zero - exponent rule: \(a^{0} = 1\) for \(a
eq0\). So \(- 9^{0}=-1\) (note that the exponent applies only to 9, not to - 9. If it were \((-9)^{0}\), it would be 1, but here it is \(-9^{0}\)).

Step3: Divide the numerator by the denominator

We have \(\frac{5^{-1}}{-9^{0}}=\frac{\frac{1}{5}}{-1}\). Dividing a number by - 1 is the same as multiplying it by - 1, so \(\frac{\frac{1}{5}}{-1}=\frac{1}{5}\times(-1)=-\frac{1}{5}\).

Answer:

\(-\frac{1}{5}\)