## Simplifying (x^7)^-3

In mathematics, simplifying expressions is a key skill. One common type of simplification involves dealing with exponents raised to other exponents. This article focuses on simplifying the expression **(x^7)^-3**.

### Understanding the Rules of Exponents

Before we tackle the simplification, let's recall the fundamental rule:

**(a^m)^n = a^(m*n)**

This rule states that when raising a power to another power, we multiply the exponents.

### Applying the Rule to (x^7)^-3

Now, let's apply this rule to our expression:

**(x^7)^-3 = x^(7 * -3)**

### Simplifying the Result

Finally, we perform the multiplication:

**x^(7 * -3) = x^-21**

### Important Note

The expression **x^-21** is the simplified form, but it can also be rewritten using the rule **a^-n = 1/a^n**:

**x^-21 = 1/x^21**

Therefore, both **x^-21** and **1/x^21** are valid simplified expressions for **(x^7)^-3**.

### Conclusion

By applying the fundamental rule of exponents, we successfully simplified **(x^7)^-3** into **x^-21** or **1/x^21**. Remember, simplifying expressions not only makes them easier to read and understand but also paves the way for further calculations and analysis.