(2x^2)^3 Simplify

Jasonbradley

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Jun 16, 2024

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Simplifying (2x^2)^3

In mathematics, simplifying expressions is a fundamental skill. Let's explore how to simplify the expression (2x^2)^3.

Understanding the Power of a Power

The expression involves a power raised to another power. This is known as the power of a power rule. The rule states that when raising a power to another power, you multiply the exponents. In other words:

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

Applying the Rule

1. Identify the base and exponents:

   • Our base is 2x^2
   • The outer exponent is 3
   • The inner exponent is 2 (in the term x^2)

2. Apply the power of a power rule:

   • (2x^2)^3 = 2^(3) * (x^2)^3

3. Simplify each term:

   • 2^(3) = 8
   • (x^2)^3 = x^(2*3) = x^6

4. Combine the simplified terms:

   • 8 * x^6 = 8x^6

Final Result

Therefore, the simplified form of (2x^2)^3 is 8x^6.