Problem 40 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(6 x^{4}\right)^{2}$$

Step-by-Step Solution

Answer

The simplified form of the expression is \(36x^8\).

Step 1: Identify base and exponent

In the expression \((6 x^{4})^{2}\), we have a base of \(6x^4\) and an exponent of 2.

Step 2: Distribute the outer exponent to each part of the base

Using the laws of exponents, we can distribute the outer exponent of 2 to both the 6 and the \(x^4\) to get \((6^2)(x^{4*2})\).

Step 3: Simplify powers

We know that \(6^2 = 36\) and \(x^8 = x^8\). Therefore \((6^2)(x^{4*2})\) simplifies to \(36x^8\).