(8a^-3)^-2/3

Jasonbradley

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Jun 16, 2024

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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 step-by-step.

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^(m-n)
• 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:

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

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

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

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

5. 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.