Simplifying (7x^3)^2
In mathematics, simplifying expressions is a fundamental skill. One common type of expression involves raising a term to a power, as in the case of (7x^3)^2. Let's break down how to simplify this expression.
Understanding the Properties of Exponents
The key to simplifying this expression lies in understanding the properties of exponents. Here's a breakdown of the relevant property:
 (a^m)^n = a^(m*n)
This property states that when raising a power to another power, you multiply the exponents.
Applying the Property

Identify the base and exponents: In our expression, the base is 7x^3 and the exponent is 2.

Apply the property: Using the property mentioned above, we can rewrite the expression as: (7x^3)^2 = 7^(32) * x^(32)

Simplify:
7^(32) * x^(32) = 7^6 * x^6
Final Result
Therefore, the simplified form of (7x^3)^2 is 7^6 * x^6. This can be further calculated if needed, but it is generally considered a simplified form.
Key Takeaways
 Remember the property of exponents for raising a power to another power.
 Apply the property carefully to each part of the base.
 Simplify the expression to its simplest form.