(-2b^-2c^3)^3

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (-2b^-2c^3)^3

This article will walk you through the steps involved in simplifying the expression (-2b^-2c^3)^3.

Understanding the Rules

To simplify this expression, we need to understand the following rules of exponents:

• Product of powers: (x^m)^n = x^(m*n)
• Negative exponents: x^-n = 1/x^n

Step-by-Step Simplification

1. Distribute the exponent: Applying the product of powers rule, we multiply the exponent outside the parentheses (3) with each exponent inside the parentheses: (-2)^3 * (b^-2)^3 * (c^3)^3

2. Simplify each term:

   • (-2)^3 = -8
   • (b^-2)^3 = b^(-2*3) = b^-6
   • (c^3)^3 = c^(3*3) = c^9

3. Combine the simplified terms: -8 * b^-6 * c^9

4. Apply the negative exponent rule: -8 * (1/b^6) * c^9

5. Final Simplified Expression: -8c^9/b^6

Conclusion

Therefore, the simplified form of the expression (-2b^-2c^3)^3 is -8c^9/b^6. By understanding and applying the rules of exponents, we can successfully simplify complex expressions like this one.