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(2x^3)^3 Simplify

2 min read Jun 16, 2024
(2x^3)^3 Simplify

Simplifying (2x^3)^3

In mathematics, simplifying expressions is a key skill. One common task is simplifying expressions involving exponents. Let's break down how to simplify the expression (2x^3)^3.

Understanding the Rules of Exponents

Before we dive into the simplification, let's recall a few fundamental rules of exponents:

  • Product of Powers: (x^m)(x^n) = x^(m+n)
  • Power of a Product: (xy)^n = x^n * y^n
  • Power of a Power: (x^m)^n = x^(m*n)

Simplifying the Expression

Now, let's apply these rules to our expression:

  1. Apply the Power of a Power rule: (2x^3)^3 = 2^3 * (x^3)^3
  2. Simplify: 2^3 * (x^3)^3 = 8 * x^(3*3)
  3. Final Result: 8 * x^(3*3) = 8x^9

Conclusion

Therefore, the simplified form of (2x^3)^3 is 8x^9. By applying the appropriate rules of exponents, we were able to manipulate the expression and arrive at a more concise form.

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