## Simplifying Expressions with Exponents

This article will explore the simplification of the expression **(x^4)^2 = x^12 / x^5** where x is not equal to 0.

### Understanding the Properties of Exponents

The problem involves two key properties of exponents:

**Power of a power:**(x^m)^n = x^(m*n)**Division of powers with the same base:**x^m / x^n = x^(m-n)

### Simplifying the Expression

Let's break down the simplification step-by-step:

**Simplify the left side:**(x^4)^2 = x^(4*2) = x^8**Simplify the right side:**x^12 / x^5 = x^(12-5) = x^7

Now we have: x^8 = x^7.

**Note:** For this equation to be true, x must be equal to 1. This is because any number raised to the power of 8 will be greater than the same number raised to the power of 7 unless that number is 1.

### Conclusion

The expression **(x^4)^2 = x^12 / x^5** simplifies to **x^8 = x^7**. This equation holds true only when **x = 1**. The key to solving this type of problem is understanding and applying the basic properties of exponents.