Problem 37 - College Algebra Essentials

Question

Simplify each exponential expression. $$\frac{x^{14}}{x^{-7}}$$

Step-by-Step Solution

Answer

The simplified form of the expression \(\frac{x^{14}}{x^{-7}}\) is \(x^{21}\).

Step 1: Understand the Rules of Exponents

Begin by understanding the rules of exponents. The rule being applied here is that when you divide two numbers with the same base, you subtract the exponents. That is, \(a^{m} / a^{n} = a^{m-n}\). Now you can apply this rule to the given problem.

Step 2: Apply the Rule to the Given Expression

Applying the rule \(a^{m} / a^{n} = a^{m-n}\), to the expression \(\frac{x^{14}}{x^{-7}}\) gives you \(x^{14-(-7)}\).

Step 3: Calculate the Result

In the expression \(x^{14-(-7)}\), subtracting a negative number is the same as adding a positive number. Therefore, the expression simplifies to \(x^{14+7}\), which is \(x^{21}\).