To simplify the expression \(\left(\frac{5}{x}\right)^{-1}\), let's follow these steps:
1. Understand the property of exponents that we will use: \(\left(\frac{a}{b}\right)^{-1} = \left(\frac{b}{a}\right)\). This property tells us that when we have a fraction raised to the power of -1, we can simply invert the fraction.
2. Apply the property to our expression:
[tex]\[
\left(\frac{5}{x}\right)^{-1} = \left(\frac{x}{5}\right)
\][/tex]
3. Now, \(\left(\frac{x}{5}\right)\) is simply the fraction with \(x\) in the numerator and 5 in the denominator. We can express this fraction in terms of powers of \(x\):
[tex]\[
\frac{x}{5} = 5^{-1} \cdot x^1
\][/tex]
4.
So the simplified expression is \(\frac{x}{5}\) or \(5^{-1} x\), which tells us that the exponent of \(x\) in the simplified expression is 1.
Therefore, the result is:
[tex]\[
x^{1}
\][/tex]
The answer is:
[tex]\[
\underline{x^{1}}
\][/tex]
