(2a^2b^3)^3/4a^3b^7

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (2a^2b^3)^3 / 4a^3b^7

This article will guide you through the process of simplifying the expression (2a^2b^3)^3 / 4a^3b^7.

Understanding the Rules

Before we begin, let's recall some fundamental rules of exponents:

• (x^m)^n = x^(m*n): When raising a power to another power, we multiply the exponents.
• x^m / x^n = x^(m-n): When dividing powers with the same base, we subtract the exponents.

Step-by-Step Simplification

1. Simplify the numerator:

   • Apply the rule (x^m)^n = x^(m*n) to the numerator:
     • (2a^2b^3)^3 = 2^3 * (a^2)^3 * (b^3)^3 = 8a^6b^9

2. Rewrite the expression:

   • The expression now becomes: 8a^6b^9 / 4a^3b^7

3. Simplify by dividing coefficients and subtracting exponents:

   • 8/4 = 2
   • a^6 / a^3 = a^(6-3) = a^3
   • b^9 / b^7 = b^(9-7) = b^2

4. Final Result:

   • The simplified expression is 2a^3b^2.

Conclusion

By applying the rules of exponents, we successfully simplified the expression (2a^2b^3)^3 / 4a^3b^7 to 2a^3b^2. This process highlights the importance of understanding these rules and applying them systematically to solve complex expressions.