2 min read Jun 17, 2024

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.


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.