Problem 30 - College Algebra Essentials

Question

Simplify each exponential expression. $$x^{-6} \cdot x^{12}$$

Step-by-Step Solution

Answer

The simplified form of \(x^{-6} \cdot x^{12}\) is \(x^{6}\)

Step 1: Identify the Base

In this expression, we have two terms being multiplied together (\(x^{-6}\) and \(x^{12}\)). Notice that the base for both terms is 'x'.

Step 2: Exponent Addition Rule

When multiplying expressions with the same base, we add the exponents together. Therefore, add the exponent \(-6\) from \(x^{-6}\) to the exponent \(12\) from \(x^{12}\). This rule is based on the properties of exponents.

Step 3: Perform the Addition

Performing the addition of \(-6\) and \(12\), we achieve \(12 - 6 = 6\). Therefore, the expression \(x^{-6} \cdot x^{12}\) can be simplified to \(x^{6}\)