(27x^3)^5/3

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (27x^3)^5/3

This article will guide you through the process of simplifying the expression (27x^3)^5/3.

Understanding the Properties of Exponents

To simplify this expression, we need to recall some key properties of exponents:

• Product of Powers Property: (a^m) * (a^n) = a^(m+n)
• Power of a Power Property: (a^m)^n = a^(m*n)
• Power of a Product Property: (a * b)^m = a^m * b^m

Simplifying the Expression

1. Apply the Power of a Power Property:

   (27x^3)^5/3 = 27^(5/3) * (x^3)^(5/3)

2. Simplify the coefficients:

   27^(5/3) = (3^3)^(5/3) = 3^(3 * 5/3) = 3^5 = 243

3. Simplify the variables:

   (x^3)^(5/3) = x^(3 * 5/3) = x^5

4. Combine the results:

   243 * x^5 = 243x^5

Conclusion

Therefore, the simplified form of the expression (27x^3)^5/3 is 243x^5. Understanding exponent properties is crucial for simplifying complex expressions and solving equations.