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Simplifying the Expression (8x³)²/³
In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (8x³)²/³.
Understanding the Properties of Exponents
The key to simplifying this expression lies in understanding the properties of exponents. Here are the relevant ones:
- Power of a power: (a^m)^n = a^(m*n)
- Fractional exponent: a^(m/n) = (a^(1/n))^m = √ⁿa^m
Applying the Properties
Let's apply these properties to our expression:
- Simplify the power of a power: (8x³)²/³ = (8² * (x³)²)/³
- Apply the power of a power again: (8² * (x³)²)/³ = (64 * x⁶)/³
- Rewrite using fractional exponent: (64 * x⁶)/³ = (64^(1/3) * x^(6/3))
- Simplify: (64^(1/3) * x^(6/3)) = 4x²
Final Result
Therefore, the simplified form of (8x³)²/³ is 4x².
Additional Notes
While we've used the specific properties of exponents, it's important to understand the general idea of simplification. It's about finding the most efficient and compact way to represent an expression. The simplified form 4x² is much easier to work with than the original expression.