Simplifying the Expression (8a^3)^2/3
This article will guide you through the process of simplifying the expression (8a^3)^2/3. We will use the rules of exponents to simplify this expression stepbystep.
Understanding the Rules of Exponents
Before we start, let's review the essential rules of exponents that we'll be using:
 Product of powers: x^m * x^n = x^(m+n)
 Quotient of powers: x^m / x^n = x^(mn)
 Power of a power: (x^m)^n = x^(m*n)
 Negative exponent: x^n = 1/x^n
 Fractional exponent: x^(m/n) = (n√x)^m
Simplifying the Expression
Let's break down the simplification process:

Apply the power of a power rule: (8a^3)^2/3 = 8^2/3 * (a^3)^2/3

Simplify the exponents: 8^2/3 * (a^3)^2/3 = 8^2/3 * a^2

Apply the negative exponent rule to 8^2/3: 8^2/3 * a^2 = 1/8^(2/3) * a^2

Simplify 8^(2/3): 1/8^(2/3) * a^2 = 1/(∛8)^2 * a^2 = 1/2^2 * a^2

Simplify the final expression: 1/2^2 * a^2 = a^2 / 4
Therefore, the simplified form of (8a^3)^2/3 is a^2 / 4.
Conclusion
By applying the rules of exponents, we have successfully simplified the expression (8a^3)^2/3. Remember to break down complex expressions into smaller steps and utilize the appropriate exponent rules. This will ensure accurate and efficient simplification.