Questions: Express the following as a single fraction involving positive exponents only. (Simplify your answer completely.) x^(-4) + x^(-5)

Solution Steps

To express the given expression as a single fraction with positive exponents, we need to find a common denominator for the terms \(x^{-4}\) and \(x^{-5}\). The common denominator will be \(x^5\). We then rewrite each term with this common denominator and combine them into a single fraction.

To combine the terms \(x^{-4}\) and \(x^{-5}\), we first identify a common denominator. The least common denominator for these terms is \(x^5\).

Next, we rewrite each term with the common denominator: \[ x^{-4} = \frac{x^1}{x^5} \quad \text{and} \quad x^{-5} = \frac{1}{x^5} \]

Now, we can combine the two fractions: \[ x^{-4} + x^{-5} = \frac{x^1}{x^5} + \frac{1}{x^5} = \frac{x + 1}{x^5} \]

Final Answer