%5E-3.jpeg "(x^7)^-3")
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.